The pth-order optimality conditions for inequality constrained optimization problems

被引：12

作者：

Brezhneva, O. A. ^{[1
]}

Tret'yakov, A. A. ^{[2
,3
]}

机构：

[1] Miami Univ, Dept Math & Stat, Oxford, OH 45056 USA

[2] Univ Podlasie Siedlce, PL-08110 Siedlce, Poland

[3] Russian Acad Sci, Ctr Comp, Moscow, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 63卷 / 5-7期

关键词：

Conditions for optimality; Nonregular optimization problems;

D O I：

10.1016/j.na.2005.02.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present pth-order necessary conditions for optimality for an optimization problem with inequality constraints in the finite-dimensional spaces. Models of this type arise as the discretization of optimal control problems, calculus of variations problems, and other problems. The paper addresses the degenerate (nonregular) case when the active constraint gradients are linearly dependent. In this case, the classical necessary conditions are either inapplicable or trivially satisfied with the zero multiplier corresponding to the objective function. The proposed high-order optimality conditions give new and nontrivial conditions for nonregular cases, and reduce to the classical conditions for regular cases. (C) 2005 Elsevier Ltd. All rights reserved.

引用

页码：E1357 / E1366

页数：10

共 50 条

[1] The pth order optimality conditions for nonregular optimization problems
Brezhneva, O. A.
Tret'yakov, A. A.
[J]. DOKLADY MATHEMATICS, 2008, 77 (02) : 163 - 165
[2] The pth order optimality conditions for nonregular optimization problems
O. A. Brezhneva
A. A. Tret’yakov
[J]. Doklady Mathematics, 2008, 77
[3] pth Order Kuhn-Tucker-Type Optimality Conditions for a Singular Inequality Constrained Optimization Problem
Tret'yakov, A. A.
[J]. DOKLADY MATHEMATICS, 2010, 82 (02) : 780 - 783
[4] pth Order Kuhn-Tucker-type optimality conditions for a singular inequality constrained optimization problem
A. A. Tret’yakov
[J]. Doklady Mathematics, 2010, 82 : 780 - 783
[5] THE P-th ORDER OPTIMALITY CONDITIONS FOR DEGENERATE INEQUALITY CONSTRAINED OPTIMIZATION PROBLEMS
Brezhneva, Olga
TreT'Yakov, Alexey A.
[J]. TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2010, 1 (02): : 198 - 223
[6] Higher order optimality conditions for inequality-constrained problems
Ivanov, Vsevolod I.
[J]. APPLICABLE ANALYSIS, 2013, 92 (12) : 2612 - 2629
[7] The p-th order necessary optimality conditions for inequality-constrained optimization problems
Brezhneva, O
Tret'yakov, A
[J]. COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2003, PT 1, PROCEEDINGS, 2003, 2667 : 903 - 911
[8] Optimality conditions for irregular inequality-constrained problems
Izmailov, AF
Solodov, MV
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 40 (04) : 1280 - 1295
[9] Optimality conditions for irregular inequality-constrained problems
Izmailov, A.F.
Solodov, M.V.
[J]. SIAM Journal on Control and Optimization, 2002, 40 (04) : 1280 - 1295
[10] Second-order optimality conditions for inequality constrained problems with locally Lipschitz data
Vsevolod I. Ivanov
[J]. Optimization Letters, 2010, 4 : 597 - 608

← 1 2 3 4 5 →