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非线性约束条件下梯度投影法的一个统一途径 总被引:2,自引:0,他引:2
对于问题(P),我们作如下假设: (H1):g_j(x)(j=1,…,m)为一阶连续可微凸函数.f(x)为一阶连续可微函数. (H2):x∈R={x|x∈E~n,g_j(x)≤0,j=1,…,m}:{g_j(x)|j∈J_J(x)}为线性无关向量组.其中J_0(x)={j|g_j(x)=0}. 自Rosen的梯度投影法产生以来,国内外流行的求解(P)的梯度投影法都是先对切面做投影,然后拉回可行域,目的是保证所取得的搜索方向为可行下降方向.1985年 相似文献
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本文通过研究几种特殊类型函数的高阶导数与原函数的求法 ,获得了由该类函数自身及其一阶导数的特征 ,即可快速写出该类函数的 n阶导数 y( n) 与原函数 y( - 1 ) 的统一公式 y( n) ( n=-1 ,1 ,2 ,3 ,… ) .该公式可给实际运算带来许多简化与方便 . 相似文献
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本文研究了有界解析函数的n阶导数估计.利用有界解析函数泰勒展开式的系数估计,得到了n阶导数估计的一般式,改进了已有的相关结果. 相似文献
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将不变子空间方法用于求解一致分数阶导数意义下的导数模型,在不变子空间方法的基础上得到了求解一致分数阶导数模型精确解的一种新方法.通过实例验证了该方法的实用性和可行性. 相似文献
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与导数有关的函数题是各省市高考年年必考的题目,形式层出不穷,且多以压轴题的身份出现许多成绩中上的考生往往处理完第一问后,对二、三问或是目的性不强的匆忙求导形成“一堆烂账”、或是手到眼不到写了一堆后发现走进了“死胡同”。 相似文献
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对于线性不等式约束的非线性规划问题,本文给出一个正基坐标向量投影方法,并在较弱的条件下证明该方法的收敛性。§1.引言考虑问题(P): 相似文献
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In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. (see Appl. Math. Comput., 80(1996), 209-224) to a broader class of non-convex programming problems. 相似文献
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本文提出一个求解多目标非线性规划问题的交互规划算法.在每一轮迭代中,此法仅要求决策者提供目标间权衡比的局部信息.算法中的可行方向是基于求解非线性规划问题的Topkis-Veinott法构千的.我们证明,在一定条件下,此算法收敛于问题的有效解. 相似文献
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An SQP method for general nonlinear programs using only equality constrained subproblems 总被引:5,自引:0,他引:5
P. Spellucci 《Mathematical Programming》1998,82(3):413-448
In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [P. Spellucci, Han's method without solving QP, in: A. Auslender, W. Oettli, J. Stoer (Eds), Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, vol. 30, Springer, Berlin, 1981, pp. 123–141.] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQP-methods, as demonstrated by extensive numcrical tests. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. 相似文献
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The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. 相似文献
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本文对具有线性约束的非线性规划问题给出一个Goldfarb方法的改进算法,并且在与[1]同样的条件下,给出了算法之超线性收敛性证明. 相似文献
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This paper gives a complete treatment of the asymptotic rate of convergence for a class of feasible directions methods, including those studied by Pironneau and Polak and by Cawood and Kostreva. Rate estimates of Pironneau and Polak are sharpened in an analysis which shows the dependence on certain parameters of the direction-finding subproblem and the problem functions. Special cases of interior optimal solution, linear constraints, and fixed matrix norm are analyzed in detail. Numerical verification is provided. 相似文献
16.
A continuation method for monotone variational inequalities 总被引:9,自引:0,他引:9
This paper presents a continuation method for monotone variational inequality problems based on a new smooth equation formulation. The existence, uniqueness and limiting behavior of the path generated by the method are analyzed.This work was supported by the National Science Foundation Presidential Young Investigator Award ECE-8552773 and by a grant from the Burlington Northern Railroad. 相似文献
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We consider a class of convex programming problems whose objective function is given as a linear function plus a convex function
whose arguments are linear functions of the decision variables and whose feasible region is a polytope. We show that there
exists an optimal solution to this class of problems on a face of the constraint polytope of dimension not more than the number
of arguments of the convex function. Based on this result, we develop a method to solve this problem that is inspired by the
simplex method for linear programming. It is shown that this method terminates in a finite number of iterations in the special
case that the convex function has only a single argument. We then use this insight to develop a second algorithm that solves
the problem in a finite number of iterations for an arbitrary number of arguments in the convex function. A computational
study illustrates the efficiency of the algorithm and suggests that the average-case performance of these algorithms is a
polynomial of low order in the number of decision variables.
The work of T. C. Sharkey was supported by a National Science Foundation Graduate Research Fellowship.
The work of H. E. Romeijn was supported by the National Science Foundation under Grant No. DMI-0355533. 相似文献
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This paper presents a secant method, based on R. B. Wilson's formula for the solution of optimization problems with inequality constraints. Global convergence properties are ensured by grafting the secant method onto a phase I - phase II feasible directions method, using a rate of convergence test for crossover control.This research was sponsored by the National Science Foundation, Grant No. ENG-73-08214 and Grant No. (RANN)-ENV-76-04264, and by the Joint Services Electronics Program. Contract No. F44620-76-C-0100. 相似文献
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A Modified SQP Method and Its Global Convergence 总被引:6,自引:0,他引:6
Guanglu Zhou 《Journal of Global Optimization》1997,11(2):193-205
The sequential quadratic programming method developed by Wilson, Han andPowell may fail if the quadratic programming subproblems become infeasibleor if the associated sequence of search directions is unbounded. In [1], Hanand Burke give a modification to this method wherein the QP subproblem isaltered in a way which guarantees that the associated constraint region isnonempty and for which a robust convergence theory is established. In thispaper, we give a modification to the QP subproblem and provide a modifiedSQP method. Under some conditions, we prove that the algorithm eitherterminates at a Kuhn–Tucker point within finite steps or generates aninfinite sequence whose every cluster is a Kuhn–Tucker point.Finally, we give some numerical examples. 相似文献
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Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization 总被引:6,自引:0,他引:6
This paper proves local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization
problems. Conditions to be satisfied at a solution are those given by the usual Jacobian uniqueness conditions. Proofs about
convergence rates are given for three kinds of step size rules. They are: (i) the step size rule adopted by Zhang et al. in
their convergence analysis of a primal-dual interior point method for linear programs, in which they used single step size
for primal and dual variables; (ii) the step size rule used in the software package OB1, which uses different step sizes for
primal and dual variables; and (iii) the step size rule used by Yamashita for his globally convergent primal-dual interior
point method for general constrained optimization problems, which also uses different step sizes for primal and dual variables.
Conditions to the barrier parameter and parameters in step size rules are given for each case. For these step size rules,
local and quadratic convergence of the Newton method and local and superlinear convergence of the quasi-Newton method are
proved.
A preliminary version of this paper was presented at the conference “Optimization-Models and Algorithms” held at the Institute
of Statistical Mathematics, Tokyo, March 1993. 相似文献