求解非线性互补问题的一个无导数下降算法

在实际求解过程中,一些非线性互补问题没有导数或很难获得导数,因此提出了无导数下降算法.通过讨论了非线性互补问题在经过价值函数的极小化变形之后的解决方法,提出求解非线性互补问题的一个无导数下降算法,在一定条件下证明了该算法的适定性及收敛性,利用数值例子表明了算法是有效的.     

计及输电约束的电力远期与现货市场联合均衡分析

针对当前国内、外电力市场的实际运营要求,研究发电商在远期合同市场和现货市场中的博弈问题,建立了一个考虑输电约束的两市场联合均衡模型。该模型所描述的均衡问题是一个具有均衡约束的均衡问题(EPEC),可用非线性互补方法求解。算例证明了模型和方法的合理性和有效性。结论显示在现货市场中以线性供应函数投标的发电商能自愿参与策略性远期合同交易,从而有效缓解其市场力,而且输电网络约束、发电成本及需求弹性等因素都会影响发电商的远期合同交易策略。     

基于非线性互补方法的现代内点最优潮流算法

提出了基于非线性互补方法的最优潮流算法。引入非线性互补函数,将内点法中KKT条件的互补松弛条件约束转化为等式约束,并采用牛顿方法求解。该方法不必保证互补松弛变量为正数,可以从任意起始点出发,具有良好的收敛性。在确定最优步长的过程中,采用了新的效益函数,节省了大量的计算时间,并有效处理了算法在收敛过程中产生的振荡问题。数值计算结果表明,提出的算法具有很好的收敛性和计算效率,对于大规模电力系统具有很好的应用前景。     

Computationally Efficient Algorithm For Frequency‐Weighted Optimal H∞ Model Reduction

In this paper, a frequency‐weighted optimal H_∞ model reduction problem for linear time‐invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize H_∞ norm of the frequency‐weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non‐convex feasibility problem. Moreover, it has been shown that the reduced‐order model is stable when both stable input and output weights are included, and its state‐space data are given explicitly by the solution of the feasibility problem. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non‐convex conditions involving rank constraint.     

The Linear Dynamic Complementarity Problem is a special case of the Extended Linear Complementarity Problem

In this paper we consider some extensions of the Linear Complementarity Problem, which is one of the fundamental problems in mathematical programming. More specifically we consider the Linear Dynamic Complementarity Problem (LDCP), the Generalized Linear Complementarity Problem (GLCP) and the Extended Linear Complementarity Problem (ELCP). In this note we show that the LDCP is a special case of the ELCP and the GLCP.     

DAE for Frictional Contact Modeling of Constrained Multi-Flexible Body Systems

A general formulation for modeling frictional contact interactions in a constrained multi-flexible body system is outlined in this paper. The governing differential-algebraic equations (DAE) for the constrained motion contains not only a frictional term but also, the unknown contact conditions. These contact conditions are characterized by a set of nonlinear complementarity equations. To demonstrate the model, a falling-spinning beam impacting a rough elastic ground with damping is solved and comparison with Stewart-Trinkles' results provided.     

计及灵活热负荷的综合能源服务商购电策略

作为未来综合能源系统背景下的能源零售主体,综合能源服务商需要对用户不同类型的需求响应（demand response, DR）资源进行有效调控,从而应对不同类型能源市场的价格波动风险,优化市场购电策略,降低能源购置成本。首先根据未来综合能源服务商的基本运营模式,构建了用户不同类型负荷响应特性模型;其次,针对综合能源服务商在运营过程中面临的主要不确定性因素,以其在不同类型市场中能源购置成本最小为目标,构建了计及DR资源的两阶段随机市场购电决策模型。最后通过算例仿真,验证了随机模型的有效性,分析了灵活供热负荷对综合能源服务商购电策略的影响。     

A direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures

This paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures. Founded on a traditional finite‐step formulation, our approach, however, avoids the typically cumbersome implementation of iterative predictor–corrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulation—cast in its most natural mathematical programming format known as a mixed complementarity problem—is directly solved by using a complementarity solver run from within a mathematical modeling system. We have chosen the industry‐standard General Algebraic Modeling System/PATH mixed complementarity problem solver that is called from within the General Algebraic Modeling System environment. We consider both von Mises and Tresca materials, with perfect or hardening (kinematic and isotropic) behaviors. Our numerical tests, five (benchmark) examples of which are presented in this paper, have been carried out using models constructed from the mixed finite element of Capsoni and Corradi (Comput. Methods Appl. Mech. Eng. 1997; 141 :67–93), which beneficially offers a locking‐free behavior and coarse‐mesh accuracy. The results indicate, in addition to an isochoric locking‐free behavior, good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of Tresca yield surfaces. Copyright © 2012 John Wiley & Sons, Ltd.     

High-accuracy finite-difference methods for the valuation of options

A finite-difference scheme often employed for the valuation of options from the Black–Scholes equation is the Crank–Nicolson (CN) scheme. The CN scheme is second order in both time and asset. For a rapid valuation with a reasonable resolution of the option price curve, it requires extremely small steps in both time and asset. In this paper, we present high-accuracy finite-difference methods for the Black–Scholes equation in which we employ the fourth-order L-stable Simpson-type (LSIMP) time integration schemes developed earlier and the well-known Numerov method for discretization in the asset direction. The resulting schemes, called LSIMP–NUM, are fourth order in both time and asset. The LSIMP–NUM schemes obtained can provide a rapid, stable and accurate resolution of option prices, allowing for relatively large steps in both time and asset. We compare the computational efficiency of the LSIMP–NUM schemes with the CN and Douglas schemes by considering valuation of European options and American options via the linear complementarity approach.     

Some iterative algorithms for the obstacle problems

In this paper we propose some iterative algorithms for the obstacle problems discretized by the finite difference method. We rewrite the obstacle problem to an equivalent complementarity problem. We use the regularization trick to non-smooth absolute function. Then we apply the Newton's method to obtain an iterative algorithm. Some other two algorithms based on this algorithm are derived. Numerical experiments show the effective of the algorithm.