一类非线性整数规则及其应用

设某县有中学n所，记为S_1,S_2…，S_i…,S_n.S_i校在校生M~（i）人，教师X_i人，     

利用遗传算法求一类非线性规划的最优解

针对一类非线性规则问题（Nonlinear Programming Problem)，采用遗传算法思想设计求解算法，实例表明，该遗传算法具有较高的计算效率。     

等式约束非线性规划的一种线性代数方程组解法

本文提出了一种求解等式约束非线性规划的新方法－线性代数方程组求解方法。我们证明了该算法具有全局收敛性和局部二阶收敛性。     

最优化中的几个问题解的等价性

考虑如下非线性规划问题：众所周知，问题（NP）的解法主要有三类：1．直接处理约束，2．将约束最优化问题化为 无约束最优化问题来处理，3．将（NP）化为简单的约束最优化问题如线性规划或二次规划等来处理，而将约束最优化问题化为无约束最优化问题的主要手段是利用如下的Lagrange函数：L（X，X，X）一八X）＋（X，g（X》十（X，h（X》（1．I）定义1．1称点卜”，V”撤足互补性条件，如果对”（X）一ojE【I：c］（亚．2）根据Lagrange函数（1．1）定义如下问题：（SPP）：求点k”，u”，v」6H””，m二。；＋c，使b“，u“，v」…     

空中防撞系统的设计

编者按：本文用相对运动的观点建立飞机两两不相撞的约束条件，将问题归结为一个非线性规划问题，用惩罚函数方法化为无约束极值问题求得最优解。罚函数选取合理，表达清楚。一、符号约定Pi为第i架飞机坐标；θi为第i架飞机方向角；rij为Pi和Pj间距；θij为Pij与X轴的夹角；v为飞机飞行速度。二、问题的分析与求解1．设计目标要设计的防撞系统中，为确保飞机不相撞，应满足如下条件：(1)安全距离要求|Pij|≥8（2）飞机偏离航向不应太远，要求|△θ|i≤30°根据上述条件及题目的要求，防撞系统的目标是达到总航向的改变最小。即min(∑|△…     

求解变量带简单界约束的非线性规划问题的信赖域方法

1．引言。本文考虑下述变量带简单界约束的非线性规划问题：问题（1．1）不仅是实际应用中出现的简单的约束最优化问题，而且相当一部分最优化问题可以把变量限制在有意义的区间内181．因此，无论在理论方面还是在实际应用方面，都有必要研究此种问题．给出简便而且有效的算法．有些文章提出了一些特殊的方法．如011和［2］．14］及16］提出了一类信赖域方法，它们都借助于某种辅助点，证明了算法的全局收敛性．在收敛速度的分析方面，除要求在＊－T点满足严格互补松弛外，它们还要求另一个条件，即在每次迭代中，辅助点的有效约束必须在尝…     

一个求线性代数方程组非负解的算法及其在线性规划中的应用

1.引言关于线性规划的多项式算法,哈奇扬于1979年首先把一个线性规划问题化成一个线性不等式组的求解问题,然后用椭球方法求解线性不等式组,并证明是多项式时间可解的。Karmarkar于1984年也给出了一个求解线性规划的多项式时间解法,他     

极小扰动约束非线性规划的最优性条件

考虑当目标函数在约束条件下的最优值作扰动时，使各约束作极小扰动的非线性规划问题．文中引进了极小扰动约束规划的极小扰动有效解概念．利用把问题归为一个相应的多目标规划问题，给出了极小扰动约束有效解的最优性条件．     

求线性规划问题相容方程组非负解的算法

本文提出一个解线性规划问题的新算法.其最优解是通过求一个相容方程组的非负解而得到.这算法的计算量在最坏情况下是O(mnτ),其中τ是相应方程的m×n矩阵非零元素的个数.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs

Recently, O(n ²) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x Dx–a x+| x–c| and (1/2)x Dx–a x+(/2)( x–c)², respectively, subject to lxb, for all nonnegative values of the parameter . Here, D is a positive diagonal n×n matrix, and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that lb. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.     

Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers.     

On ℓp programming

Our paper treats the primal and dual program of ?_p programming. ?_p programming is a generalization of ?_p approximation problems. There is a strict connection between ?_p programming and geometrical programming, because in both of them geometrical inequality plays a fundamental role. The structure of our paper follows that of Klafszkys [1].In the first Sections duality theorems are proved, which play an important role in mathematical programming. Most of these results can be found in Petersons and Eckers [3,4,5], but our proofs are much more simple and we show these fundamental properties more detailed.Afterwards the relation between the Lagrange function and the optimal solution pair is investigated. Regularity is investigated as well and we show the marginal value of ?_p programming. In the end linear programming ?_p constrained ?_p approximation problems, the quadratically constrained quadratic programming and compromise programming are shown as special cases of ?_p programming.     

Composite geometric programming

Geometric programming is based on functions called posynomials, the terms of which are log-linear. This class of programs is extended from the composition of an exponential and a linear function to an exponential and a convex function. The resulting duality theory for composite geometric programs retains many of the qualities of geometric programming duality, while at the same time encompassing new areas of application. As an application, composite geometric programming is applied to exponential geometric programming. A pure dual is developed for the first time and used to solve a problem from the literature.This research was supported by the Air Force Office of Scientific Research, Grant No. AFOSR-83-0234.     

The relationship between integer and real solutions of constrained convex programming

We prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs.     

A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors.     

A note on article “A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function”

Kim and Whang use a tolerance approach for solving fuzzy goal programming problems with unbalanced membership functions [J.S. Kim, K. Whang, A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function, European Journal of Operational Research 107 (1998) 614–624]. In this note it is shown that some results in that article are incorrect. The necessary corrections are proposed.     

A linear programming approach for linear programs with probabilistic constraints

We study a class of mixed-integer programs for solving linear programs with joint probabilistic constraints from random right-hand side vectors with finite distributions. We present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs. We provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed-integer formulation of Luedtke et al. (2010) [13] as well as via lower bounds produced by their cutting plane method. While we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics, we also prove that the theoretical worst-case solution quality for these algorithms is arbitrarily far from optimal. Our computational study compares our heuristics against both the extended mixed-integer programming formulation and the cutting plane method of Luedtke et al. (2010) [13]. Our heuristics efficiently and consistently produce solutions with small optimality gaps, while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5%.