A Weak Maximum Principle for Discrete Optimal Control Problems with Mixed Constraints

被引：0

作者：

Andreani, Roberto ^{[1
]}

Ascona, John Frank Matos ^{[2
]}

de Oliveira, Valeriano Antunes ^{[3
]}

机构：

[1] State Univ Campinas Unicamp, Dept Appl Math, Campinas, SP, Brazil

[2] State Univ Mato Grosso UNEMAT, Fac Exact & Technol Sci, Sinop, MT, Brazil

[3] Sao Paulo State Univ UNESP, Inst Biosci, Humanities & Exact Sci, Rua Cristovao Colombo, N 2265, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 203卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Discrete optimal control problems; Mixed constraints; Nondegenerate necessary optimality conditions; Discrete maximum principle; Constant rank of the subspace component constraint qualification;

D O I：

10.1007/s10957-024-02524-0

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this study, first-order necessary optimality conditions, in the form of a weak maximum principle, are derived for discrete optimal control problems with mixed equality and inequality constraints. Such conditions are achieved by using the Dubovitskii-Milyutin formalism approach. Nondegenerate conditions are obtained under the constant rank of the subspace component (CRSC) constraint qualification, which is an important generalization of both the Mangasarian-Fromovitz and constant rank constraint qualifications. Beyond its theoretical significance, CRSC has practical importance because it is closely related to the formulation of optimization algorithms. In addition, an instance of a discrete optimal control problem is presented in which CRSC holds while other stronger regularity conditions do not.

引用

页码：562 / 599

页数：38

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