On one class of optimal control problems for quantum systems

We present a new modification of the global control improvement method based on a known Krotov’s method for optimal control in quantum systems from a certain class. The algorithm is implemented for high-dimensional systems as a parallel program. We give computations for the control in a quantum dynamical system that represents a well-known model of communicating the quantum state in spin chains.     

Solution and investigation of one class of inexact integer programming problems

We give a formulation of an integer programming problem with inexact constraint matrix coefficients and an inexact objective function. An approach to solution and investigation of such inexact integer programming problems is proposed.Translated from Kibernetika, No. 2, pp. 42–46, 64, March–April, 1989.     

Defining the asymptotics for one class of singularly perturbed problems of vibrational mechanics

In this paper, a solution algorithm for the optimal control problem for the system with uncertain dynamics which is the asymptotics of the singularly perturbed system with fast oscillator is proposed.     

Global minimization of indefinite quadratic problems

A branch and bound algorithm is proposed for finding the global optimum of large-scale indefinite quadratic problems over a polytope. The algorithm uses separable programming and techniques from concave optimization to obtain approximate solutions. Results on error bounding are given and preliminary computational results using the Cray 1S supercomputer as reported.     

Comparison of two methods for the solution of a class of nonconvex energy problems using convex minimization algorithms

Nonmonotone, possibly multivalued stress-strain or reaction-displacement laws give rise to hemivariational inequalities. Due to the lack of convexity and the nonsmoothness of the underlying (super)potentials the problems generally have nonunique solutions (stable or unstable). In this paper we propose two methods for the solution of the hemivariational inequality problem. The first method is based on the decomposition of the nonconvex superpotential into convex constituents. The second one uses an iterative scheme in order to approximate the hemivariational inequality problem with a sequence of variational inequality problems. Both methods are based on the solution of convex subproblems and constitute an effective, reliable and versatile family of numerical algorithms for large scale hemivariational inequalities. Finally, the two methods are applied to solve the same problem and the obtained results are compared.     

On one class of model optimization problems with a continuum of solutions

We consider critical sets of an H-regular functional. We propose a condition under which the set of all critical points forms a critical set. We discuss several problems that lead to such sets and show a connection with the notion of Morse index. As examples we consider integral functionals for functions defined on a segment.     

Categorical properties of solvability for one class of minimization problems<Superscript>1</Superscript>

A lower semicontinuous functional disturbed by a Minkowski functional of a closed bounded convex neighborhood of zero possessing the Kadets–Klee property is minimized on a closed subset X of a reflexive Banach space E. It is proved that the set of parameters for which the problem has a solution contains a G_δ-subset dense in E \ X. It is shown that the reflexivity condition and the condition of the Kadets–Klee property of the neighborhood cannot be weakened. The application to optimization problems for linear systems with vector performance criteria is considered.     

Complexity of optimal scheduling problems with three jobs

We consider the time-optimal scheduling problemn/m/J of n jobs with fixed routes on m machines. The problem3/m/J/ with identical routes and the problem3/5/J/ are shown to be NP-hard. Similar results are obtained for the problem of minimizing the mean processing time of three jobs on m machines.Translated from Kibernetika, No. 5, pp. 50–54, September–October, 1990.     

On numerical solution of one class of inverse problems for discontinuous dynamic systems

Consideration was given to a class of problems that are inverse to the dynamic processes described by the discontinuous systems of ordinary differential equations changing their form depending on the membership of the current process state to one or another subdomain of the state space. In this problem, it is both the object parameters and the surfaces themselves defining the boundaries of the sub-domains where the differential equations retain their form that are identified as the object parameters.     

A study of one class of NLP problems arising in parametric semi-infinite programming

The paper deals with a nonlinear programming (NLP) problem that depends on a finite number of integers (parameters). This problem has a special form, and arises as an auxiliary problem in study of solutions' properties of parametric semi-infinite programming (SIP) problems with finitely representable compact index sets. Therefore, it is important to provide a deep study of this NLP problem and its properties w.r.t. the values of the parameters. We are especially interested in the case when optimal solutions of the NLP problem satisfy certain properties due to some specific requirements arising in parametric SIP. We establish the values of the parameters for which optimal solutions of the corresponding NLP problem fulfil the needed properties, and suggest an algorithm that determines the right values of the parameters. An example is proposed to illustrate the application of the algorithm.     

Developing feasible and optimal schedules of jobs on one machine

The paper considers the properties of feasible and optimal scheduling of jobs on one machine under constraints on the terms of the beginning and completion of jobs and on partial sequences of job performance. The established properties and the lower-bound estimates of the length of the optimal schedule are used to develop methods for the exact and approximate solutions of the formulated problem by sequential optimization algorithms. The proposed algorithms are illustrated by numerical examples and can be successfully applied to solve these problems in the absence of constraints.