An Adaptive Neural Network Model for Nonlinear Programming Problems

In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.     

Computational limit analysis of rigid-plastic bodies in plane strain

This paper deals with the computational methods for limit analysis of plane strain problems. The finite element mathematical programming formula (FE-MPF) for determining the upper bound load multiplier established by the authors earlier is adopted and modified for plane strain problems. The penalty method is used to impose the incompressibility constraint. The FE-MPF is solved by a direct iteration procedure without the need of a searching process. This algorithm is not sensitive to the volumetric locking effect. And it can be easily extended to the limit analysis of three dimensional problems. The results of numerical examples are satisfactory and show the stable convergency of the present algorithm.     

多目标规划的对偶二阶条件

本文针对多目标规划 ( VP)的 Lagrange对偶规划 ( VD) ,从几何直观的角度出发 ,给出对偶规划( VD)的二阶最优性条件 ,即对偶二阶条件 ,并证明了相应的最优性定理 .     

A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control

Shift schemes are commonly used in non-convex situations when solving unconstrained discrete-time optimal control problems by the differential dynamic programming (DDP) method. However, the existing shift schemes are inefficient when the shift becomes too large. In this paper, a new method of combining the DDP method with a shift scheme and the steepest descent method is proposed to cope with non-convex situations. Under certain assumptions, the proposed method is globally convergent and has q-quadratic local conve rgence. Extensive numerical experiments on many test problems in the literature are reported. These numerical results illustrate the robustness and efficiency of the proposed method.     

Duality and martingales: a stochastic programming perspective on contingent claims

The hedging of contingent claims in the discrete time, discrete state case is analyzed from the perspective of modeling the hedging problem as a stochastic program. Application of conjugate duality leads to the arbitrage pricing theorems of financial mathematics, namely the equivalence of absence of arbitrage and the existence of a probability measure that makes the price process into a martingale. The model easily extends to the analysis of options pricing when modeling risk management concerns and the impact of spreads and margin requirements for writers of contingent claims. However, we find that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options. An extension of the model to incorporate pre-existing liabilities and endowments reveals the reasons why buyers and sellers trade in options. The model also indicates the importance of financial equilibrium analysis for the understanding of options prices in incomplete markets. Received: June 5, 2000 / Accepted: July 12, 2001?Published online December 6, 2001     

求0-1型整数规划的一种新方法

本文给出求 0 -1型整数规划的一种新方法 ,该方法利用对所有目标函数值排序的方法 ,求出最优解 .该方法简单易行且计算量较小     

Solving Fuzzy Variational Inequalities

This paper studies the variational inequality problem over a fuzzy domain and variational inequalities for fuzzy mappings over a fuzzy domain. It is shown that such problems can be reduced to bilevel programming problems. A penalty function algorithm is introduced with a convergence proof. Numerical examples are also included to illustrate the solution procedure.     

An interactive method for multiple-objective mathematical programming problems

An interactive method is developed for solving the general nonlinear multiple objective mathematical programming problems. The method asks the decision maker to provide partial information (local tradeoff ratios) about his utility (preference) function at each iteration. Using the information, the method generates an efficient solution and presents it to the decision maker. In so doing, the best compromise solution is sought in a finite number of iterations. This method differs from the existing feasible direction methods in that (i) it allows the decision maker to consider only efficient solutions throughout, (ii) the requirement of line search is optional, and (iii) it solves the problems with linear objective functions and linear utility function in one iteration. Using various problems selected from the literature, five line search variations of the method are tested and compared to one another. The nonexisting decision maker is simulated using three different recognition levels, and their impact on the method is also investigated.