一类特殊多项式整数规划问题的最优化算法

本文考虑了一类特殊的多项式整数规划问题。此类问题有很广泛的实际应用,并且是NP难问题。对于这类问题,最优性必要条件和最优性充分条件已经给出。我们在本文中将要利用这些最优性条件设计最优化算法。首 先,利用最优性必要条件,我们给出了一种新的局部优化算法。进而我们结合最优性充分条件、新的局部优化算法和辅助函数,设计了新的全局最优化算法。本文给出的算例展示出我们的算法是有效的和可靠的。     

一个改进的序列二次规划可行下降算法及其全局收敛性

利用广义投影校正技术对搜索方向进行某种修正,改进假设条件,采用一种新型的一阶修正方向并结合SQP技术,建立了求解非线性约束最优化问题(p)的一个新的SQP可行下降算法,在较温和的假设条件下证明了算法的全局收敛性.由于新算法仅需较小的存储,从而适合大规模最优化问题的计算.     

求解无约束最优化问题的非奇异Broyden算法的全局收敛性

求解无约束最优化问题的非奇异Ｂｒｏｙｄｅｎ算法的全局收敛性李董辉（湖南大学应用数学系）ＧＬＯＢＡＬＣＯＮＶＥＲＧＥＮＣＥＯＦＮＯＮＳＩＮＧＵＬＡＲＢＲＯＹＤＥＮ＇ＳＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＵＮＣＯＮＳＴＲＡＩＮＥＤＯＰＴＩＭＩＺＡｆＩＯＮＳ￥...     

DFP算法的全局收敛性分析

1引言理论分析和大量数值试验表明，在求解（1．1）的各种算法中，拟Newton法是效果最好的一类方法．DFP算法是最早提出的拟Newton法，它首先由Davidon［2］给出并由Fletcher和Powell【3］修改DFP算法的计算步骤如下：算法1．1．1”．取二R”，BIE＊”“”对称正定，k：＝1．2”．计算gb＝7八kh），若gb—0，则终止，得解kk．否则，转入下一步．3O．dk——BK‘gb．4“．进行线搜索确定步长aa．在上面的算法中，步长0。的确定有两种方式：其一，精确线搜索，即。。满足：其M，非精确线搜索．本文考察WOlfe线搜索，即a＆满足：其中o…     

一个全局最优化问题的填充函数

本文给出了一个非线性全局最优化问题的填充函数定义,此定义不同于以前已有的填充函数定义。根据此定义,本文提出了一簇单参数填充函数和相应的填充函数算法．对几个算例的数据测试表明,该填充函数法是可行和有效的．     

全局最优化问题的一个无参数的填充函数算法

本文研究了全局最优化问题.利用构造填充函数的方法,提出了一个新的无参数填充函数,它是目标函数的一个明确表达式.得到了一个新的无参数填充函数算法,数值试验结果表明该填充函数算法是有效的,从而推广了填充函数算法在求解全局最优化问题方面的应用.     

在一个新步长规则下梯度投影算法的全局收敛性

考虑约束最优化问题：minx∈Ωf(x)其中:f:R^n→R是连续可微函数，Ω是一闭凸集。本文研究了解决此问题的梯度投影方法，在步长的选取时采用了一种新的策略，在较弱的条件下，证明了梯度投影响方法的全局收敛性。     

一类新的信赖域算法的全局收敛性

本文对于无约束最优化问题提出了一类非单调的信赖域算法，它是通常的单调信赖域算法的推广。当目标函数是有下界的连续可微函数，而且它的二阶导数的近似的模是线性地依赖于迭代次数时，我们证明了新算法的整体收敛性。     

求解正定二次规划的一个全局收敛的滤子内点算法

现有的大多数分类问题都能转化成一个正定二次规划问题的求解.通过引入滤子方法,并结合求解非线性规划的原始对偶内点法,给出求解正定二次规划的滤子内点算法.该算法避免了使用效益函数时选取罚因子的困难,在较弱的假设条件下,算法具有全局收敛性.     

一类求解MPEC的全局收敛性算法

概述MPEC求解上存在的困难；提出将求解普通约束优化问题的信赖域方法用于求解MPEC；在适当条件下建立算法的全局收敛性定理。     

A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique

This paper is concerned with the development of an algorithm to solve continuous polynomial programming problems for which the objective function and the constraints are specified polynomials. A linear programming relaxation is derived for the problem based on a Reformulation Linearization Technique (RLT), which generates nonlinear (polynomial) implied constraints to be included in the original problem, and subsequently linearizes the resulting problem by defining new variables, one for each distinct polynomial term. This construct is then used to obtain lower bounds in the context of a proposed branch and bound scheme, which is proven to converge to a global optimal solution. A numerical example is presented to illustrate the proposed algorithm.     

A deterministic algorithm for global optimization

We present an algorithm for finding the global maximum of a multimodal, multivariate function for which derivatives are available. The algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope. Successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy. The algorithm has been implemented in RATFOR and execution times for standard test functions are presented at the end of the paper.Partially supported by NSF DMS-8718362.     

基于随机搜索的一个约束优化问题的全局收敛算法

讨论了具有一般约束的全局优化问题,给出该问题的一个随机搜索算法,证明了该算法依概率1收敛到问题的全局最优解．数值结果显示该方法是有效的．     

线性约束三次规划问题的全局最优性必要条件和最优化算法

讨论了带线性不等式约束三次规划问题的最优性条件和最优化算法. 首先, 讨论了带有线性不等式约束三次规划问题的 全局最优性必要条件. 然后, 利用全局最优性必要条件, 设计了解线性约束三次规划问题的一个新的局部最优化算法(强局部最优化算法). 再利用辅助函数和所给出的新的局部最优化算法, 设计了带有线性不等式约束三 规划问题的全局最优化算法. 最后, 数值算例说明给出的最优化算法是可行的、有效的.     

多点收缩混沌优化方法及全局收敛性证明

针对目前混沌优化算法在选取局部搜索空间时的盲目性,提出一种具有自适应调节局部搜索空间能力的多点收缩混沌优化方法.该方法在当前搜索空间搜索时保留多个较好搜索点,之后利用这些点来确定之后的局部搜索空间,以达到对不同的函数和当前搜索空间内已进行搜索次数的自适应效果.给出了该算法以概率1收敛的证明.仿真结果表明该算法有效的提高了混沌优化算法的性能,改善了混沌算法的实用性.     

An algorithm for solving global optimization problems with nonlinear constraints

In this paper we propose an algorithm using only the values of the objective function and constraints for solving one-dimensional global optimization problems where both the objective function and constraints are Lipschitzean and nonlinear. The constrained problem is reduced to an unconstrained one by the index scheme. To solve the reduced problem a new method with local tuning on the behavior of the objective function and constraints over different sectors of the search region is proposed. Sufficient conditions of global convergence are established. We also present results of some numerical experiments.     

A modified integral global optimization method and its asymptotic convergence

In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.     

An interval algorithm for constrained global optimization

An interval algorithm for bounding the solutions of a constrained global optimization problem is described. The problem functions are assumed only to be continuous. It is shown how the computational cost of bounding a set which satisfies equality constraints can often be reduced if the equality constraint functions are assumed to be continuously differentiable. Numerical results are presented.     

A global optimization approach for solving the convex multiplicative programming problem

We consider a convex multiplicative programming problem of the form% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaGG7bGaam% OzamaaBaaaleaacaaIXaaabeaakiaacIcacaWG4bGaaiykaiabgwSi% xlaadAgadaWgaaWcbaGaaGOmaaqabaGccaGGOaGaamiEaiaacMcaca% GG6aGaamiEaiabgIGiolaadIfacaGG9baaaa!4A08!\[\{ f_1 (x) \cdot f_2 (x):x \in X\} \]where X is a compact convex set of ⁿ and f ₁, f ₂ are convex functions which have nonnegative values over X.Using two additional variables we transform this problem into a problem with a special structure in which the objective function depends only on two of the (n+2) variables. Following a decomposition concept in global optimization we then reduce this problem to a master problem of minimizing a quasi-concave function over a convex set in ² ₂. This master problem can be solved by an outer approximation method which requires performing a sequence of simplex tableau pivoting operations. The proposed algorithm is finite when the functions f _i, (i=1, 2) are affine-linear and X is a polytope and it is convergent for the general convex case.Partly supported by the Deutsche Forschungsgemeinschaft Project CONMIN.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.