Optimization of System of Nonlinear Second Order Differential Inequalities

TL;DR

This paper develops a comprehensive framework for optimizing systems governed by nonlinear second order differential inequalities, providing necessary and sufficient optimality conditions, discretization techniques, and numerical validation.

Contribution

It introduces a novel discretization approach and equivalence theorems for subdifferential inclusions to analyze complex nonlinear inequality systems.

Findings

Derived necessary and sufficient optimality conditions

Established discretization methods for nonlinear inequalities

Validated theoretical results with a numerical example

Abstract

This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality. According to proposed discretization method and equivalence theorems for subdifferential inclusions, the problem with a system of discrete-approximation inequalities are investigated which highly contributes to the derivation of adjoint discrete inclusions generated by given system of nonlinear inequality constraints. Moreover, in the limit case, we obtain sufficient conditions for optimality of the continuous problem. A numerical example is presented to illustrate the theoretical result.