运输问题的一种图上解法

把运输问题转化成图的问题，给出了求解运输问题的一种图上算法。通过实例，验证了这是一个有效，可行的方法。     

基于突变评价法的研究型大学知识创新综合评价

如何评价研究型大学知识创新是建设创新型国家过程中一个亟待解决的现实问题。本文首先在分析各种评价方法、研究型大学知识创新系统的构成及其特点的基础上，介绍了突变评价法的基本思想和步骤，随后利用突变评价法，建立了研究型大学知识创新综合评价指标体系，并对北京地区的12所大学进行综合评价，得出合理的评价结果，证明突变评价法是一种可行的综合评价方法。     

演化均匀优化算法

针对演化算法，使用随机法产生初始点带来的缺陷和均匀设计方法的优点，提出了演化均匀优化算法，进行了算法收敛性分析，并把它应用于多峰函数的数值优化计算，给出了计算示例，结果表明该方法是一种可行而且有效的优化算法．     

一种加性AHP法的构造及应用

首先分析了 Satty的传统 AHP法的缺陷 ,然后给出了加性 AHP法的构造原理及权值求法 ,并以一实例说明加性 AHP法在多指标决策分析中的应用 .最后指出加性 AHP法是一种较之传统 AHP法更方便可行的方法 .     

内点惩罚函数法的改进算法

本文针对内点惩罚函数法现有算法在计算中设计变量常常越出可行域边界 ,导致计算失效而提出了一种改进的计算方法 .该方法的主导思想就是保证对内点惩罚函数的求极值过程一直限定在可行设计区域内 ,从而保证各 X* ( γ* )均在可行域内 ,并进行了实例计算验证 .     

一种迭代平差法

本文以解决水准网的平差问题为例,提出一种迭代平差法,简单可行.此方法与最小二乘法没有联系,因而也不需要解法方程组.     

非线性约束优化问题的混合粒子群算法

把处理约束条件的一个外点方法和改进的粒子群优化算法相结合,提出了一种求解非线性约束优化问题的混合粒子群优化算法.该方法兼顾了粒子群优化和外点法的优点,对算法迭代过程中出现不可行粒子,利用外点法处理后产生可行粒子.数值实验表明了提出的新算法具有有效性、通用性和稳健性.     

内点惩罚函数法的改进算法

本针对内点惩罚函数法现有算法在计算设计变量常常越出可行域边界,导致计算失效而提出了一种改进的计算方法。该方法的主要思想就是保证对内点惩罚函数的求极值过程一直限定在可行设计区域内,从而保证各X^-(γ^*)均在可行域内,并进行了实例计算验证。     

一种多指标决策与评价的新方法

指出了多指标决策与评价投影法所用的决策矩阵无量纲化方法的不妥之处及在应用中存在的问题 ,提出了一种新方法 ,并用实例说明了该方法是可行合理的 .     

线性红束最优化问题的一族次可行方向法

本文给出线性红束最优化问题的一族算法，方法具有如下特点：１）初始迭代点可以任意选取；２）一旦有某一个迭代点进入可行域，方法将成为一族可行方向法；３）算法避开不易处理的罚函数和罚参数，文中采用一种最优性控制函数将初始化阶段和最优化阶段有机地结合起来，正是这种技巧保证了算法的全局收敛性。     

A feasible direction method for linear programming

We discuss a finite method of a feasible direction for linear programming problems. The method begins with a feasible basic vector for the problem, constructs a profitable direction to move using the updated column vectors of the nonbasic variables eligible to enter this basic vector. It then moves in this direction as far as possible, while retaining feasibility. This move in general takes it though the relative interior of a face of th set of a feasible solutions. The final point, $\text{x}$, obtained at the end of this move will not in general be a basic solution. Using $\text{x}$ the method then constructs a basic feasible solution at which the objective value is better than, or the same as that at $\text{x}$. The whole process repeats with the new basic feasible solution. We show that this method can be implemented using basis inverses. Initial computer runs of this method in comparison with the usual edge following primary simplex algorithms are very encouraging.     

A convergent criss-cross method

Our paper presents a new Criss-Cross method for solving linear programming problems. Starting from a neither primal nor dual feasible solution, we reach an optimal solution in finite number of steps if it exists. If there is no optimal solution, then we show that there is not primal feasible or dual feasible solution, We prove the finiteness of this procedure. Our procedure is not the same as the primal or dual simplex method if we have a primal or dual feasible solution, so we have constructed a quite new procedure for solving linear programming problems.     

A class of methods for linear programming

A class of methods is presented for solving standard linear programming problems. Like the simplex method, these methods move from one feasible solution to another at each iteration, improving the objective function as they go. Each such feasible solution is also associated with a basis. However, this feasible solution need not be an extreme point and the basic solution corresponding to the associated basis need not be feasible. Nevertheless, an optimal solution, if one exists, is found in a finite number of iterations (under nondegeneracy). An important example of a method in the class is the reduced gradient method with a slight modification regarding selection of the entering variable.     

Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.     

An efficient feasible SQP algorithm for inequality constrained optimization

In this paper, an efficient feasible SQP method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. Per single iteration, it is only necessary to solve one QP subproblem and a system of linear equations with only a subset of the constraints estimated as active. In addition, its global and superlinear convergence are obtained under some suitable conditions.     

The Complex Interior-Boundary method for linear and nonlinear programming with linear constraints

In this paper we develop the Complex method; an algorithm for solving linear programming (LP) problems with interior search directions. The Complex Interior-Boundary method (as the name suggests) moves in the interior of the feasible region from one boundary point to another of the feasible region bypassing several extreme points at a time. These directions of movement are guaranteed to improve the objective function. As a result, the Complex method aims to reach the optimal point faster than the Simplex method on large LP programs. The method also extends to nonlinear programming (NLP) with linear constraints as compared to the generalized-reduced gradient.The Complex method is based on a pivoting operation which is computationally efficient operation compared to some interior-point methods. In addition, our algorithm offers more flexibility in choosing the search direction than other pivoting methods (such as reduced gradient methods). The interior direction of movement aims at reducing the number of iterations and running time to obtain the optimal solution of the LP problem compared to the Simplex method. Furthermore, this method is advantageous to Simplex and other convex programs in regard to starting at a Basic Feasible Solution (BFS); i.e. the method has the ability to start at any given feasible solution.Preliminary testing shows that the reduction in the computational effort is promising compared to the Simplex method.     

A feasible direction method for image restoration

In this work, a feasible direction method is proposed for computing the regularized solution of image restoration problems by simply using an estimate of the noise present on the data. The problem is formulated as an optimization problem with one quadratic constraint. The proposed method computes a feasible search direction by inexactly solving a trust region subproblem with the truncated Conjugate Gradient method of Steihaug. The trust region radius is adjusted to maintain feasibility and a line-search globalization strategy is employed. The global convergence of the method is proved. The results of image denoising and deblurring are presented in order to illustrate the effectiveness and efficiency of the proposed method.     

A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points

In many engineering optimization problems, the objective and the constraints which come from complex analytical models are often black-box functions with extensive computational effort. In this case, it is necessary for optimization process to use sampling data to fit surrogate models so as to reduce the number of objective and constraint evaluations as soon as possible. In addition, it is sometimes difficult for the constrained optimization problems based on surrogate models to find a feasible point, which is the premise of further searching for a global optimal feasible solution. For this purpose, a new Kriging-based Constrained Global Optimization (KCGO) algorithm is proposed. Unlike previous Kriging-based methods, this algorithm can dispose black-box constrained optimization problem even if all initial sampling points are infeasible. There are two pivotal phases in KCGO algorithm. The main task of the first phase is to find a feasible point when there is no feasible data in the initial sample. And the aim of the second phase is to obtain a better feasible point under the circumstances of fewer expensive function evaluations. Several numerical problems and three design problems are tested to illustrate the feasibility, stability and effectiveness of the proposed method.     

Regularization of L ∞-Optimal Control Problems for Distributed Parameter Systems

We consider L -norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.     

A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization

In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained minimization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method.