求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.     

Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

解可分离约束双凹规划问题的一种外逼近方法[英文]

在本文中，我们提出了双凹规划问题和更一般的广义凹规划问题。我们给出了双凹规划问题的整体最优性条件，并构造了一个有限终止外逼近算法。     

Generalized Constraint Qualifications and Optimality Conditions for Set-Valued Optimization Problems

In this paper we discuss the connections of four generalized constraint qualifications for set-valued vector optimization problems with constraints. Then some K-T type necessary and sufficient optimality conditions are derived, in terms of the contingent epiderivatives.     

Testing the ℜ- strategy for a Reverse Convex Problem

This paper is devoted to solving a reverse-convex problem. The approach presented here is based on Global Optimality Conditions. We propose a general conception of a Global Search Algorithm and develop each part of it. The results of numerical experiments with the dimension up to 400 are also given. This revised version was published online in July 2006 with corrections to the Cover Date.     

带非凸二次约束的二次比式和问题的全局优化算法(英文)

对带非凸二次约束的二次比式和问题(P)给出分枝定界算法,首先将问题(P)转化为其等价问题(Q),然后利用线性化技术,建立了(Q)松弛线性规划问题(RLP),通过对(RLP)可行域的细分及求解一系列线性规划问题,不断更新(Q)的上下界,从理论上证明了算法的收敛性,数值实验表明了算法的可行性和有效性.     

The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function

This paper studies the two-dimensional layout optimization problem.An optimization model withperformance constraints is presented.The layout problem is partitioned into finite subproblems in terms ofgraph theory,in such a way of that each subproblem overcomes its on-off nature optimal variable.A minimaxproblem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we presentthe optimality function for every subproblem and prove that the first order necessary optimality condition issatisfied at a point if and only if this point is a zero of optimality function.     

Existence of Solutions of a Vector Optimization Problem with a Generic Lower Semicontinuous Objective Function

We study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of lower semicontinuous bounded-from-below objective functions . We establish the existence of a G _δ everywhere dense subset ℱ of such that, for any objective function belonging to ℱ, the corresponding minimization problem possesses a solution.     

A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem

The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported.     

Minimizing a Linear Objective Function with Fuzzy Relation Equation Constraints

An minimization problem with a linear objective function subject to fuzzy relation equations using max-product composition has been considered by Loetamonphong and Fang. They first reduced the problem by exploring the special structure of the problem and then proposed a branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we provide a necessary condition for an optimal solution of the minimization problems in terms of one maximum solution derived from the fuzzy relation equations. This necessary condition enables us to derive efficient procedures for solving such optimization problems. Numerical examples are provided to illustrate our procedures.     

An Algorithm for Solving Optimization Problems with One Linear Objective Function and Finitely Many Constraints of Fuzzy Relation Inequalities

An optimization model with one linear objective function and fuzzy relation equation constraints was presented by Fang and Li (1999) as well as an efficient solution procedure was designed by them for solving such a problem. A more general case of the problem, an optimization model with one linear objective function and finitely many constraints of fuzzy relation inequalities, is investigated in this paper. A new approach for solving this problem is proposed based on a necessary condition of optimality given in the paper. Compared with the known methods, the proposed algorithm shrinks the searching region and hence obtains an optimal solution fast. For some special cases, the proposed algorithm reaches an optimal solution very fast since there is only one minimum solution in the shrunk searching region. At the end of the paper, two numerical examples are given to illustrate this difference between the proposed algorithm and the known ones.     

三维多箱异构货物装载优化及其可视化

针对七种现实约束的集装箱三维多箱异构货物装载优化问题,提出了一种基于 “块”和“空间”的启发式搜索算法。算法采用树搜索策略,根据可用空间,对每一次搜索的货物块进行评估,得到最佳的货物块,直到无可用空间或无可装载的货物为止。基于开放式标准测试数据的计算结果表明,该算法在时间效率和体积利用率上均优于已有的同类研究。并基于Net平台开发了一款3D装箱布局优化可视化软件,已在相关物流企业中得到推广应用,验证了算法的实用性。     

条形装箱问题的优化模型和增广Lagrange算法

This paper formulates a two-dimensional strip packing problem as a non-linear programming(NLP)problem and establishes the first-order optimality con-ditions for the NLP problem.A numerical algorithm for solving this NLP problemis given to find exact solutions to strip-packing problems involving up to 10 items.Approximate solutions can be found for big-sized problems by decomposing the setof items into small-sized blocks of which each block adopts the proposed numericalalgorithm.Numerical results show that the approximate solutions to big-sized prob-lems obtained by this method are superior to those by NFDH,FFDH and BFDHapproaches.     

优化方法解决无上层约束的线性双层规划问题

In this paper we propose an optimal method for solving the linear bilevel programming problem with no upper-level constraint. The main idea of this method is that the initial point which is in the feasible region goes forward along the optimal direction firstly. When the iterative point reaches the boundary of the feasible region, it can continue to go forward along the suboptimal direction. The iteration is terminated until the iterative point cannot go forward along the suboptimal direction and effective direction, and the new iterative point is the solution of the lower-level programming. An algorithm which bases on the main idea above is presented and the solution obtained via this algorithm is proved to be optimal solution to the bilevel programming problem. This optimal method is effective for solving the linear bilevel programming problem.     

框式凸二次规划问题的非精确不可行内点算法

对框式凸二次规划问题提出了一种非精确不可行内点算法 ,该算法使用的迭代方向仅需要达到一个相对的精度 .在初始点位于中心线的某邻域内的假设下 ,证明了算法的全局收敛性     

The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker-Akhiezer Function

We obtain a simple sufficient condition for the solvability of the Riemann factorization problem for matrix-valued functions on a circle. This condition is based on the symmetry principle. As an application, we consider nonlinear evolution equations that can be obtained by a unitary reduction from the zero-curvature equations connecting a linear function of the spectral parameter z and a polynomial of z. We consider solutions obtained by dressing the zero solution with a function holomorphic at infinity. We show that all such solutions are meromorphic functions on ℂ _xt ² without singularities on ℝ _xt ² . This class of solutions contains all generic finite-gap solutions and many rapidly decreasing solutions but is not exhausted by them. Any solution of this class, regarded as a function of x for almost every fixed t ∈ ℂ, is a potential with a convergent Baker-Akhiezer function for the corresponding matrix-valued differential operator of the first order.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 453–471, September, 2005.     

求解两块可分离凸极小化问题的惯性交替方向乘子法

The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.     

Quasistability of a Vector Trajectory Majority Optimization Problem

We consider a multicriteria combinatorial problem with majority optimality principle whose particular criteria are of the form MINSUM, MINMAX, and MINMIN. We obtain a lower attainable bound for the radius of quasistability of such a problem in the case of the Chebyshev norm on the space of perturbing parameters of the vector criterion. We give sufficient conditions for the quasistability of the problem; these are also necessary in the case of linear special criteria.     

An optimal control problem for a pest, predator, and plant system

The paper is devoted to an optimal control problem for a system of three nonlinear parabolic equations from population dynamics. The equations model a trophic chain consisting of a predator, a pest and a plant species. The existence and uniqueness of the positive solution for the system are proved. The control variable is connected with the action of a pesticide. Our goal is to minimize the density of the pest and to maximize the plant density. The existence of the optimal solution is proved. The first and second order optimality conditions are established.     

Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables.We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.