Necessary Optimality Conditions for Continuous-Time Optimization Problems with Equality and Inequality Constraints

TL;DR

This paper derives first and second order necessary optimality conditions for continuous-time optimization problems with constraints, using regularity conditions and an implicit function theorem.

Contribution

It introduces a comprehensive set of necessary optimality conditions for constrained continuous-time problems, employing a novel regularity condition and an implicit function theorem approach.

Findings

Established first and second order necessary conditions.

Utilized a full rank regularity condition.

Applied an uniform implicit function theorem.

Abstract

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit function theorem are used in order to establish such necessary conditions.