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.     

一种改进的GDF多目标优化算法

本文提出一种交互式非线性多目标优化算法，该算法是ＧＤＦ多目标优化算法的改进，具有这样的特点：算法采用了既约设计空间策略，具有良好的收敛性；算法生成的迭代点是有效解；算法具有多种一维搜索准则；对于线性多目标问题，算法只需一次交互迭代即可示出多目标问题的最优解。     

城市配送车辆路径优化集束式算法的客户点归并策略

VRP问题的研究起步较早,求解方法也非常丰富,然而,面对客户规模庞大,交通网络复杂的多约束车辆优化调度问题,现有算法显得无能为力.为有效解决需求点规模庞大的城市配送车辆优化调度问题,提出一种新的两阶段启发式算法——集束式算法,采用"集中后分派,分派后扩展"的思想,对末梢客户和同路段客户进行客户点合并,从全局上降低搜索范围,并提出相关客户点归并算法.     

无约束优化问题的一个下降方法

本文研究了无约束优化问题.利用当前和前面迭代点的信息以及曲线搜索技巧产生新的迭代点,得到了一个新的求解无约束优化问题的下降方法.在较弱条件下证明了算法具有全局收敛性.当目标函数为一致凸函数时,证明了算法具有线性收敛速率.初步的数值试验表明算法是有效的.     

基于数论的总体优化随机搜索算法

本文研究了多峰函数的总体优化问题.提出了基于数论的总体优化随机搜索算法,证明了算法依概率1收敛到总体极值点,并给出了计算示例.     

一类非线性规划问题的信赖域内点算法

本文对约束为线性的一类非线性优化问题提出了一种依赖域内点算法的,其中约束非负性要求一个仿射变换阵实现,其子问题变成了与个带仿射变换的线性等式约束的求解,我们证明了算法的有效性,在一定条件下证明了由算法产生的序列收敛到优化总理２的一阶稳定,点。     

一类新的曲线搜索下的多步下降算法

提出一类新的曲线搜索下的多步下降算法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率.算法利用前面多步迭代点的信息和曲线搜索技巧产生新的迭代点,收敛稳定,不用计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.     

组合优化算法中摆脱局部极小值的几种策略

局部搜索算法是一种非常有效的求解组合优化问题的算法,它具有通用、灵活等特点。但是,由于搜索空间和目标函数的复杂性,目标函数在搜索空间中有许多局部极小值点,使算法在这些局部极小值点处被“卡住”,大大影响算法的效果。对于此问题,笔查阅了大量献资料,结合自己的研究实践,总结出几种跳出局部极小“陷井”的策略,使用这些策略,有望使算法更加完善,在求解组合优化问题过程中更能发挥其作用。     

一类无约束复合非光滑优化的信赖域算法

本文提出了一个易实施的处理一类无约束复合非光滑优化的信赖域算法，并在一定条件下证明了该算法所产生的迭代序列的任何聚点都是原问题的稳定点．     

复合凸优化的快速邻近点算法

在大数据时代,随着数据采集手段的不断提升,大规模复合凸优化问题大量的出现在包括统计数据分析,机器与统计学习以及信号与图像处理等应用中.本文针对大规模复合凸优化问题介绍了一类快速邻近点算法.在易计算的近似准则和较弱的平稳性条件下,本文给出了该算法的全局收敛与局部渐近超线性收敛结果.同时,我们设计了基于对偶原理的半光滑牛顿法来高效稳定求解邻近点算法所涉及的重要子问题.最后,本文还讨论了如何通过深入挖掘并利用复合凸优化问题中由非光滑正则函数所诱导的非光滑二阶信息来极大减少半光滑牛顿算法中求解牛顿线性系统所需的工作量,从而进一步加速邻近点算法.     

A restart algorithm for computing fixed points without an extra dimension

An algorithm to compute a fixed point of an upper semicontinuous point to set mapping using a simplicial subdivision is introduced. The new element of the algorithm is that for a given grid it does not start with a subsimplex but with one (arbitrary) point only; the algorithm will terminate always with a subsimplex. This subsimplex yields an approximation of a fixed point and provides the starting point for a finer grid. Some numerical results suggest that this algorithm converges more rapidly than the known algorithms. Moreover, it is very simple to implement the algorithm on the computer.     

一个关于二次规划问题的分段线性同伦算法

本文发展了一个关于二次规划问题的分段线性同伦算法。该算法可看作是外点罚函数法的一个变体。凡是符合外点罚函数法收敛条件的二次规划问题用该算法均可经有限次轮回运算得到稳定解。大量的关于随机的凸二次规划问题的数值实验结果表明它的计算效率是高的，在某些条件下可能是多项式时间算法。     

一类线性与框式约束凸规划问题的原始-对偶内点算法

本文对一类具有线性和框式约束的凸规划问题给出了一个原始-对偶内点算法, 该算法可在任一原始-对偶可行内点启动, 并且全局收敛,当初始点靠近中心路径时, 算法成为中心路径跟踪算法。 数值实验表明, 算法对求解大型的这类问题是有效的。     

一类求解凸规划的鞍点法

根据凸规划的Kuhn-Tucker定理,有a)假如(x~*,y~*)是L(x,y)在D上的鞍点,那么 (1)x~*是(CP)问题的最优解,     

Deepest point of a polyhedron and linear programming

Abstract

The problem of finding a deepest point (a ball centre) of a polyhedron is studied. A finite combinatorial interior point method is presented for this problem which yields an algorithm for linear programming. We conjecture that this is a strongly polynomial algorithm. Meanwhile developing the algorithm, several auxiliary results were found; among others, Gorokh and Werner’s algorithm for linear inequalities is slightly extended. Our numerical experiments with the problem detected bugs in a linear interior point solver used in MATLAB 6 Optimization Toolbox.     

A Proximal Point-Type Method for Multicriteria Optimization

In this paper, we present a proximal point algorithm for multicriteria optimization, by assuming an iterative process which uses a variable scalarization function. With respect to the convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is that our paper gets full convergence for quasi-convex functions. In the convex or pseudo-convex cases, we prove convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm, obtaining the iterative step through an unconstrained subproblem. Then, we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem.     

一种基于邻近点算法的变步长原始-对偶算法

本文考虑求解一种源于信号及图像处理问题的鞍点问题.基于邻近点算法的思想,我们对原始-对偶算法进行改进,构造一种对称正定且可变的邻近项矩阵,得到一种新的原始-对偶算法.新算法可以看成一种邻近点算法,因此它的收敛性易于分析,且无需较强的假设条件.初步实验结果表明,当新算法被应用于求解图像去模糊问题时,和其他几种主流的高效算法相比,新算法能得到较高质量的结果,且计算时间也是有竞争力的.     

A stochastic steepest-descent algorithm

A stochastic steepest-descent algorithm for function minimization under noisy observations is presented. Function evaluation is done by performing a number of random experiments on a suitable probability space. The number of experiments performed at a point generated by the algorithm reflects a balance between the conflicting requirements of accuracy and computational complexity. The algorithm uses an adaptive precision scheme to determine the number of random experiments at a point; this number tends to increase whenever a stationary point is approached and to decrease otherwise. Two rules are used to determine the number of random experiments at a point; one, in the inner loop of the algorithm, uses the magnitude of the observed gradient of the function to be minimized; and the other, in the outer-loop, uses a measure of accumulated errors in function evaluations at past points generated by the algorithm. Once a stochastic approximation of the function to be minimized is obtained at a point, the algorithm proceeds to generate the next point by using the steepest-descent deterministic methods of Armijo and Polak (Refs. 3, 4). Convergence of the algorithm to stationary points is demonstrated under suitable assumptions.     

Computer programs for non‐linear programming

In this paper we consider the problem of maximizing a non‐linear or linear objective function subject to non‐linear and/or linear constraints. The approach used is an adaptive random search with some non‐random searches built‐in. The algorithm begins with a given point which is replaced by another point if the latter satisfies each of the constraints and results in a bigger functional value. The process of moving from one point to a better point is repeated many times. The value of each of the coordinates of the next point is determined by one of several ways; for example, a coordinate is sometimes forced to have the same value as the value of the corresponding coordinate of the current feasible point. In this algorithm, a candidate point receives no further computational considerations as soon as it is found to be unfeasible; this makes the algorithm general. Computer programs illustrating the details of the new algorithm are given and computational results of two numerical test problems from the literature are presented. Optimality was reached in each of these two problems.     

有向网络中具有一个枢纽点的最小支撑树的计算方法

对有向网络中具有一个枢纽点的支撑树的问题和性质进行了研究,给出了在有向网络图中寻找以某一定点为枢纽点的最小支撑树的计算方法,并对算法的复杂性进行了讨论,最后将该算法应用于实际算例的计算．