Necessary conditions for continuous-time optimization under the Mangasarian–Fromovitz constraint qualification

ABSTRACT

In this paper, a Mangasarian–Fromovitz-type regularity condition is presented with the purpose of obtaining first order necessary optimality conditions for continuous-time nonlinear programming problems with both equality and inequality constraints. The Karush–Kuhn–Tucker-type optimality conditions are obtained by means of geometric ideas, where a theorem of the alternative and a uniform implicit function theorem are the main tools.

KEYWORDS:

• Continuous-time programming
• necessary conditions
• constraint qualifications
• Mangasarian–Fromovitz conditions

AMS CLASSIFICATIONS:

• 90C30
• 90C46

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Moisés Rodrigues Cirilo do Monte http://orcid.org/0000-0002-0436-769X

Valeriano Antunes de Oliveira  http://orcid.org/0000-0003-3613-3801

Additional information

Funding

This work was supported by the São Paulo Research Foundation (FAPESP, Brazil) [grants numbers 2013/07375-0 and 2016/03540-4]; and the National Council for Scientific and Technological Development (CNPq, Brazil) [grant numbers 457785/2014-4 and 310955/2015-7].