Approximation error in PDE-based modelling of vehicular platoons

We study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation, as was done in Barooah, Mehta, and Hespanha [Barooah, P., Mehta, P.G., and Hespanha, J.P. (2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]), ‘Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability’, IEEE Transactions on Automatic Control, 54, 2100–2113], Hao, Barooah, and Mehta [Hao, H., Barooah, P., and Mehta, P.G. (2011), ‘Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure’, IEEE Transactions on Automatic Control, 56, 923–929]. In particular, we examine the difference between the stability margins of the coupled-ordinary differential equations (ODE) model and its partial differential equation (PDE) approximation, which we call the approximation error. The stability margin is defined as the absolute value of the real part of the least stable pole. The PDE model has proved useful in the design of distributed control schemes (Barooah et al. 2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]; Hao et al. 2011 Hao, H, Barooah, P and Mehta, PG. 2011. Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure. IEEE Transactions on Automatic Control, 56: 923–929. [Crossref], [Web of Science ®] , [Google Scholar]); it provides insight into the effect of gains of local controllers on the closed-loop stability margin that is lacking in the coupled-ODE model. Here we show that the ratio of the approximation error to the stability margin is O(1/N), where N is the number of vehicles. Thus, the PDE model is an accurate approximation of the coupled-ODE model when N is large. Numerical computations are provided to corroborate the analysis.     

Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000 Fliess, M and Marquez, R. 2000. Continuous-time Linear Predictive Control and Flatness: A Module-theoretic Setting with Examples. International Journal of Control, 73: 606–623. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b Hagenmeyer, V and Delaleau, E. 2003b. Exact Feedforward Linearization Based on Differential Flatness. International Journal of Control, 76: 537–556. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.     

Comment on ‘Persistent inputs and the standard H2-multivariable control problem’ by K. Park and J.J. Bongiorno Jr

It is necessary to welcome the publication of the paper by Park and Bongiorno Jr (Park, K. and Bongiorno Jr, J.J. (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Persistent Inputs and the Standard H₂-multivariable Control Problem’, International Journal of Control, 82, 2002–2012) in which the special cases in H₂-optimisation problems are considered. However, for correct orientation of readers we would like to note some publications which, in our opinion, are connected to a problem given by Park and Bongiorno Jr (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), but are absent there.     

Adaptive learning control design for robotic manipulators driven by permanent magnet synchronous motors

On the basis of the ideas recently presented in Tomei and Verrelli (Tomei, P., and Verrelli, C.M. (2010 Tomei, P and Verrelli, CM. 2010. Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance. International Journal of Control, 83: 1515–1528. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance’, International Journal of Control, 83, 1515–1528) and Marino et al. (Marino, R., Tomei, P., and Verrelli, C.M. (2011 Marino, R, Tomei, P and Verrelli, CM. 2011. Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties. International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720 [Google Scholar]), ‘Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties’, International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720), we briefly show how the adaptive learning control design proposed in Liuzzo and Tomei (Liuzzo, S., and Tomei, P. (2009 Liuzzo, S and Tomei, P. 2009. Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback. International Journal of Adaptive Control and Signal Processing, 23: 97–109.  [Google Scholar]), Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback, International Journal of Adaptive Control and Signal Processing, 23, 97–109) can be extended to robotic manipulators driven by nonsalient-pole (surface) permanent magnet synchronous motors. Unstructured uncertain dynamics (that is no parameterisation is available for the uncertainties) of the rigid robot with rotational joints are considered as well as uncertainties in stator resistances of the synchronous motors are taken into account. Two solutions with clear stability proofs are presented: a global decentralised control via state feedback and a semi-global control via output feedback. Output tracking of known periodic reference signals and learning of corresponding uncertain input reference signals are achieved. Available results in the literature are thus improved since no simplification concerning negligible electrical motor dynamics is used.     

A parallel time-memory tradeoff attack on the Hill cipher

Leap et al. (2016 Leap, T., T. McDevitt, K. Novak, and N. Siermine. 2016. Further improvements to the Bauer-Millward attack on the Hill cipher. Cryptologia 40:1–16.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) reduced the time complexity of the Bauer-Millward (2007 Bauer, C., and K. Millward. 2007. Cracking matrix encryption row by row. Cryptologia 31(1):76–83.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) ciphertext-only attack on the Hill cipher from 𝒪(Lⁿ) to 𝒪(L^n?1), where L is the length of the alphabet, and n is the block size. This article presents an attack that reduces the complexity to 𝒪(L^n?1?s), 0?≤?s?≤?n???1. The practical limitation on the size of s is the memory available on the computer being used for the attack. Specifically, the computer must be able to hold L^s integer arrays of length N, where N is the number of blocks of ciphertext. The key idea is not to iterate over potential rows of the decryption matrix, but to iterate over randomly chosen characters in the plaintext. This attack also admits a straightforward parallel implementation on multiple processors to further decrease the run time of the attack.     

Mapping the image

The Brainstorm feature introduced in Adobe After Effects CS3 (2007) allows users to automate parts of the process of generating design variations for the purposes of comparison and selection. The paper begins with a brief discussion of current discursive formations around software and software-based practice among digital design practitioners and educators. Next, the paper draws upon critical concepts drawn from multimodal discourse analysis, media theory and sociology to analyse Brainstorm in terms of the interplay of software structure and design agency. The key concepts used are modality, articulation and interpretation (Kress and van Leeuwen 1996 Kress, G. and van Leeuwen, T. 1996. Reading images: the grammar of visual design, London: Routledge.  [Google Scholar], 2001), the database as cultural form and the logic of selection (Manovich 2001 Manovich, L. 2001. The language of new media, Cambridge, MA: MIT Press.  [Google Scholar]), habitus and practical logic (Bourdieu 1977 Bourdieu, P. 1977. Outline of a theory of practice, New York: Cambridge University Press. [Crossref] , [Google Scholar]) and the radius of creativity (Toynbee 2000 Toynbee, J. 2000. Making popular music: musicians, creativity and institutions, London: Arnold.  [Google Scholar]). Throughout, the paper addresses specific structural features of the software, thus developing an overview of the affordances and constraints of Brainstorm as a creative tool.     

Comment on ‘Optimal inventory replenishment policy for the EPQ model under trade credit derived without derivatives’

In this article, we complement the shortcoming of the inventory economic production quantity (EPQ) model developed by Huang and Huang (2008 Huang, YF and Huang, HF. 2008. Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives. International Journal of Systems Science, 39: 539–546. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives’, International Journal of Systems Science, 39, 539–546), and propose an arithmetic–geometric inequality method to obtain the global optimal solution without taking complex differential calculus or using tedious algebraic manipulations. Finally, we provide an economical interpretation of the theoretical result so that the reader can understand the insight of the result.     

A continuous review inventory model with controllable backorder rate and investments

In this study, we investigate a continuous review inventory model to reduce lead time, yield variability and setup cost simultaneously through capital investments. We assume that the backorder rate is depending on the length of the lead time through the amount of shortages. We also assume that lead time demand's distribution is not known but its first and second moments are known. We apply minimax distribution free procedure to minimise the expected total annual cost. By using logarithmic investment function we describe the relationship between the reduction in lead time, yield variability and setup cost with capital investment. This function was used in many existing models. Our main aim is to determine the optimal capital investment and ordering policies that minimises the expected total annual cost. To find out the optimal solution, an algorithm is given. With the help of this algorithm, optimal capital investment and ordering policies are wrought out. Numerical examples are given to elucidate the model. Our proposed model greatly differs from the model existing in the literature (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])) viz: (1) In the above model, yield variability and setup cost were reduced through capital investment. In our model we reduce yield variability setup cost and also the lead time, which plays a vital role in any business. By reducing lead time we can improve the service level to the customer so as to increase the competitive edge in business. (2) In the model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), it was assumed that lead time demand follows normal distribution. But in our model we take the distribution of lead time demand as distribution free. That is, it can follow any distribution which is more general. (3) In the above model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), shortages are completely backlogged. But we consider partial backlogging and take the backlogging rate as 0 ≤ B ≤ 1. If we set backlogging rate B = 1 we get the above model. That is, the above model is particular case of our model. (4) We also assume that the backorder rate depends on the length of the lead time through the amount of shortages. If the lead time is longer then shortage accumulation is higher. The patience of customers will result in failure in business since some customers may turn to some other supplier. Hence, the backorder rate will be reduced. This assumption is very realistic.     

A Novel High Quality High Capacity Image Hiding Scheme Based on Image Compression and an Optical Pixel Adjustment Process

ABSTRACT

Image hiding methods embed a secret image into a host image. The resultant stego-image does not attract the interceptors that would not detect the differences between the host image and the stego-image. To exploit the great developments in the area of image compression and to improve the quality of stego-image, this paper proposes a new method to embed the secret image into the host image. Basically, the secret image is compressed and then embedded into host image. The embedding method is based on the Optimal Pixel Adjustment Process (OPAP) and genetic algorithm. In the paper we addressed the important issues to build such systems. The experimental results showed that the proposed method can improve the quality from 60% to 80% when compared with the simple Least Significant Bit (LSB) replacement methods. Adding to that, the mean square error of the stego-image is much lower compared with other methods (Chan & Cheng, 2004 Chan, C.K. and Cheng, L.M. 2004. Hiding data in images by simple LSB substitution. Pattern Recognition, 37(3): 469–474. [Crossref], [Web of Science ®] , [Google Scholar]; Chang, Hsiao, & Chan, 2003 Chang, C.C., Hsiao, J.Y. and Chan, C.S. 2003. Finding optimal least-significant-bit substitution in image hiding by dynamic programming strategy. Pattern Recognition, 36(7): 1583–1595. [Crossref], [Web of Science ®] , [Google Scholar]; Thien & Lin, 2003 Thien, C.C. and Lin, J.C. 2003. A simple and high-hiding capacity method for hiding digit-by-digit data in images based on modulus function. Pattern Recognition, 36(12): 2875–2881. [Crossref], [Web of Science ®] , [Google Scholar]; Tseng, Chan, Ho, & Chu, 208; Wang, Lin, & Lin, 2001 Wang, R.Z., Lin, C.F. and Lin, J.C. 2001. Image hiding by optimal LSB substitution and genetic algorithm. Pattern Recognition, 34(3): 671–683. [Crossref], [Web of Science ®] , [Google Scholar]). Also, the proposed technique improves capacity. In other words, we can embed a secret image with size 450?×?450 inside a hosting image with size 512?×?512.     

Asymptotically fast polynomial matrix algorithms for multivariable systems

We present the asymtotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank; nullspace; determinant; generic inverse reduced form (Giorgi et al. 2003, Storjohann 2003 Storjohann, A. 2003. “High-order lifting and integrality certification”. In J. Symb. Comp. Edited by: Giusti, M and Pardo, LM. Vol. 36, 613–648. Nice, France, 3, , USA Special issue International Symposium on Symbolic and Algebraic Computation (ISSAC’2002). Guest editors: [Google Scholar], Jeannerod and Villard 2005 Jeannerod, C-P and Villard, G. 2005. Essentially optimal computation of the inverse of generic polynomial matrices. J. Comp., 21: 72–86.  [Google Scholar], Storjohann and Villard 2005 Storjohann, A and Villard, G. July 2005. “Computing the rank and a small nullspace basis of a polynomial matrix”. In Proc. International Symposium on Symbolic and Algebraic Computation, 309–316. Beijing, China: ACM Press.  [Google Scholar]). We show that they essentially can be reduced to two computer algebra techniques, minimal basis computations and matrix fraction expansion/reconstruction, and to polynomial matrix multiplication. Such reductions eventually imply that all these problems can be solved in about the same amount of time as polynomial matrix multiplication. The algorithms are deterministic, or randomized with certified output in a Las Vegas fashion.     

A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games

This paper provides a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by Engwerda (2003 Engwerda, JC. 2003. Solving the scalar feedback Nash algebraic Riccati equations: an eigenvector approach. IEEE Trans. Automat. Contr., 48: 847–853. [Crossref] , [Google Scholar]) to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations.     

Knowledge processes in virtual teams: consolidating the evidence

This article takes stock of the current state of research on knowledge processes in virtual teams (VTs) and consolidates the extent research findings. Virtual teams, on the one hand, constitute important organisational entities that facilitate the integration of diverse and distributed knowledge resources. On the other hand, collaborating in a virtual environment creates particular challenges for the knowledge processes. The article seeks to consolidate the diverse evidence on knowledge processes in VTs with a specific focus on identifying the factors that influence the effectiveness of these knowledge processes. The article draws on the four basic knowledge processes outlined by Alavi and Leidner (2001 Alavi, M.Leidner, D.E., 2001. Review: knowledge management and knowledge management systems: conceptual foundations and research issues. MIS Quarterly, 25 (1), 107–136. doi: 10.2307/3250961[Crossref], [Web of Science ®] , [Google Scholar]) (i.e. creation, transferring, storage/retrieval and application) to frame the investigation and discuss the extent research. The consolidation of the existing research findings allows us to recognise the gaps in the understanding of knowledge processes in VTs and identify the important avenues for future research.     

Optimal control of the production–inventory system with deteriorating items and tradable emission permits

Using the well-known Arrow and Karlin (1958) Arrow, K.J., and Karlin, S. (1958), ‘Production over Time with Increasing Marginal Costs’, in Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow and S. Karlin, Stanford: Stanford University Press, pp. 61–69. [Google Scholar] dynamic production–inventory model and the model with tradable emission permits which was presented by Dobos (2005 Dobos, I. (2005), ‘The Effects of Emission Trading on Production and Inventories in the Arrow–Karlin Model’, International Journal of Production Economics, 93–94, 301–308.[Crossref], [Web of Science ®] , [Google Scholar], 2007) Dobos I. (2007), ‘Tradable Emission Permits and Production-inventory Strategies of the Firm’, International Journal of Production Economics, 108, 329–333.[Crossref], [Web of Science ®] , [Google Scholar], we develop a model of the production–inventory system with deteriorating items and tradable emission permits. The objective of this paper is to apply the optimal control theory to solve the production–inventory problem with deteriorating items and tradable emission permits, and derive the optimal inventory level and the optimal production rate that minimise the total cost. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the production–inventory system is carried out.     

CIPHER EQUIPMENT

Abstract

In this article, a simplified version of the International Data Encryption Algorithm (IDEA) is described. This simplified version, like simplified versions of DES [8-12 Schaefer , E. 1996 . “A Simplified Data Encryption Standard Algorithm,” Cryptologia , 20 ( 1 ): 77 – 84 . Schneier , B. 1996 . Applied Cryptography, , 2nd ed . Wiley , New York , NY . Schneier , B. 1999. Crypto Guru Bruce Schneier Answers. http://slashdot.org/interviews/99/10/29/0832246.shtml last accessed February 23, 2007. Shannon , C. “Communications Theory of Secrecy Systems,” Oct. 1949 . Bell Systems Technical Journal , 28 ( 4 ): 656 – 715 . Trappe , W. and L. Washington . 2006 . Introduction to Cryptography with Coding Theory, , 2nd ed. Prentice Hall , Upper Saddle River , NJ . ] and AES [6 Musa , M. , E. Shaefer , and S. Wedig . 2003 . “A Simplified AES Algorithm and its Linear and Differential Cryptanalysis,” Cryptologia , 17 ( 2 ): 148 – 177 . [Google Scholar] 7 Phan , R. 2002 . “Mini Advanced Encryption Standard (Mini-AES): A Testbed for Cryptanalysis Students,” Cryptologia , 26 ( 4 ): 283 – 306 .[Taylor &; Francis Online] , [Google Scholar]] that have appeared in print, is intended to help students understand the algorithm by providing a version that permits examples to be worked by hand. IDEA is useful teaching tool to help students bridge the gap between DES and AES.     

Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative

In this article, we extend a Milstein finite difference scheme introduced in 8 Giles, M. B. and Reisinger, C. 2012. Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. SIAM Financ. Math., 3(1): 572–592. (doi:10.1137/110841916)[Crossref] , [Google Scholar] for a certain linear stochastic partial differential equation (SPDE) to semi-implicit and fully implicit time-stepping as introduced by Szpruch 32 Szpruch, L. 2010. Numerical approximations of nonlinear stochastic systems PhD Thesis, University of Strathclyde [Google Scholar] for stochastic differential equations (SDEs). We combine standard finite difference Fourier analysis for partial differential equations with the linear stability analysis in 3 Buckwar, E. and Sickenberger, T. 2011. A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods. Math. Comput. Simulation, 81: 1110–1127. (doi:10.1016/j.matcom.2010.09.015)[Crossref], [Web of Science ®] , [Google Scholar] for SDEs to analyse the stability and accuracy. The results show that Crank–Nicolson time-stepping for the principal part of the drift with a partially implicit but negatively weighted double Itô integral gives unconditional stability over all parameter values and converges with the expected order in the mean-square sense. This opens up the possibility of local mesh refinement in the spatial domain, and we show experimentally that this can be beneficial in the presence of reduced regularity at boundaries.     

A prototype Greek text to Greek Sign Language conversion system

In this article, a prototype Greek text to Greek Sign Language (GSL) conversion system is presented. The system is integrated into an educational platform that addresses the needs of teaching GSL grammar and was developed within the SYNENNOESE project (Efthimiou et al. 2004a Efthimiou, E. 2004a. “Developing an e-learning platform for the Greek sign language”. In Computer helping people with special needs, Lecture Notes in Computer Science Edited by: Miesenberger, K., Klaus, J. and Zagler, W. Vol. 3118, 1107–1113.  [Google Scholar]. Developing an e-learning platform for the Greek sign language. In: K. Miesenberger, J. Klaus, and W. Zagler, eds. Computer helping people with special needs, Lecture Notes in Computer Science, Springer-Verlag, vol. 3118, 1107–1113). The detailed implementation of the language-processing component of a Greek text to GSL conversion system is provided, focusing upon the inherent problems of knowledge elicitation of sign language (SL) grammar and its implementation within a parser framework. It is based on an SL dictionary (Efthimiou et al. 2004a Efthimiou, E. 2004a. “Developing an e-learning platform for the Greek sign language”. In Computer helping people with special needs, Lecture Notes in Computer Science Edited by: Miesenberger, K., Klaus, J. and Zagler, W. Vol. 3118, 1107–1113.  [Google Scholar]) database of coded GSL knowledge. The proposed system has been designed and implemented after considering most state-of-the-art SL machine translation or Conversion systems, such as Vsigns (Papadogiorgaki et al. 2004 Papadogiorgaki, M. VSigns – a virtual sign synthesis web tool. Proceedings of Sixth COST 276 Workshop on Information and Knowledge Management for Integrated Media Communication. May2004, Thessaloniki, Greece.  [Google Scholar]. VSigns – a virtual sign synthesis web tool. In: Proceedings of Sixth COST 276 Workshop on Information and Knowledge Management for Integrated Media Communication, May 2004, Thessaloniki, Greece), ZARDOZ (Veale et al. 1998 Veale, T., Conway, A. and Collins, B. 1998. The challenges of cross-modal translation: English to sign language translation in the ZARDOZ system. Machine Translation, 13: 81–106. [Crossref] , [Google Scholar]. The challenges of cross-modal translation: English to sign language translation in the ZARDOZ system. Machine Translation, 13, 81–106) and SignSynth (Angus 2001 Angus, G. S.B. 2001. “SignSynth: a sign language synthesis application using Web3D and Perl”. In Gesture and Sign Language in Human–Computer Interaction, London, , UK: International Gesture Workshop.  [Google Scholar]. SignSynth: a sign language synthesis application using Web3D and Perl. In: Gesture and Sign Lanauage in Human–Computer Interaction. London, UK: International Gesture Workshop), and taking into account their advantages and disadvantages. The overall architecture is innovative since other existing systems either do not consider the GSL or they cannot be effectively applied on sentences but just on single words. The system is demonstrable on any conventional PC.     

A new predicto-corrector method for pseudomonotone nonlinear complementarity problems

Based on the Logarithmic-Quadratic Proximal (LQP) method 2 Auslender, A., Teboulle, M. and Ben-Tiba, S. 1999. A logarithmic-quadratic proximal method for variational inequalities. Comput. Optim. Appl., 12: 31–40. [Crossref], [Web of Science ®] , [Google Scholar], we propose a new prediction-correction method for nonlinear complementarity problem (NCP). We obtain the predictor through a simplified inexact logarithmic-quadratic proximal method under a relaxed inexact criterion. The corrector is obtained by the improved extragradient method. Under certain conditions, the global convergence of the proposed method is proved. Preliminary numerical results indicate the efficiency of the proposed method.