基于存档策略的多目标优化的遗传算法及其收敛性分析

设计了一种用遗传算法求解多目标优化问题的有效方法——基于存档策略的多目标优化的遗传算法,并讨论了此算法的收敛性.首先给出档案的定义,设计出基于支配关系下的带有存档策略遗传算法,并通过算例检验了算法的有效性;然后引入了两档案间的距离的概念,在此距离定义的基础上证明了算法在概率意义下是收敛的.     

Duality for Dini-Invex Nonsmooth Multiobjective Programming

In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Dini invex functions are discussed. On the base of this, we study the Wolfe type duality and Mond-Weir type duality for Dini-invex nonsmooth multiobjective programmings and obtain corresponding duality theorems.     

非光滑伪线性多目标规划对偶

本文利用Ｄｉｎｉ右上、右下导数给出了非光滑伪线性多目标规划的对偶理论，建立了Ｍｏｎｄ－Ｗｅｉｒ型对仍与Ｗｏｌｆ型对偶；并证明了原问题与对偶问题之间的对偶定理．     

非线性互补问题的组合同伦算法

针对拟P_*-映射和P(τ,α,β)-映射所对应的非线性互补问题,本文对其解的存在性及有效求解算法进行了研究.文中利用组合同伦方法给出了这两类非线性互补问题存在有界解的构造性证明,并利用预估校正方法对同伦路径进行跟踪,得到了互补问题的解.通过数值算例验证了该算法的有效性.     

A Combined Homotopy Interior Point Method for Nonconvex Programming with Pseudo Cone Condition

ＳｉｎｃｅＫａｒｍａｒｋａｒ ｓｆａｍｏｕｓｐａｐｅｒ [1 ]ｏｎａｎｅｗ ｐｏｌｙｎｏｍｉａｌｉｎｔｅｒｉｏｒｐｏｉｎｔａｌｇｏｒｉｔｈｍｆｏｒｌｉｎｅａｒｐｒｏｇｒａｍｍｉｎｇｗａｓｐｕｂｌｉｓｈｅｄｉｎ 1 984 ,ｉｎｔｅｒｉｏｒｐｏｉｎｔｍｅｔｈｏｄｓｈａｖｅｂｅｅｎｐｒｏｖｅｎｔｏｂｅａｃｌａｓｓｏｆｅｆｆｉｃｉｅｎｔｍｅｔｈｏｄｓｆｏｒｍａｔｈｅｍａｔｉｃａｌｐｒｏｇｒａｍｍｉｎｇａｎｄｈａｖｅｂｅｅｎｐａｉｄｍｕｃｈａｔｔｅｎｔｉｏｎ .Ｕｐｔｏｎｏｗ ,ｔｈｅｏｒｉｅｓ,ａｌｇｏｒｉｔｈｍｓａ…     

求解多目标规划最小弱有效解的同伦内点方法

本文利用非线性规划中的组合同伦方法;给出了求解目标规划问题最小弱有效解的同伦内点方法,并证明了该方法是整体收敛的。     

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions , we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.     

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING*

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.     

弱拟法锥条件下非凸优化问题的同伦算法

本文给出弱拟法锥条件的定义,并针对非线性组合同伦方程,得到在弱拟法锥条件下求解约束非凸优化问题的同伦内点算法.证明了该算法对于可行域的某个子集中几乎所有的点,同伦路径存在,并且同伦路径收敛于问题的K-K-T点,通过数值例子验证了该算法是有效的.     

约束序列极大极小问题的凝聚同伦内点方法

本文研究了拟法锥条件下的约束序列极大极小问题,利用凝聚函数把目标函数及部分约束条件进行带参数的磨光,再利用同伦方法在拟法锥条件下,构造性地证明了广义K-K-T方程解的存在性,并且对几乎所有的可行域内点作为初值,凝聚同伦内点法生成的同伦路径以广义K-K-T方程的解为极限点.