G-penalty approach for multi-dimensional control optimisation problem with nonlinear dynamical system

Abstract

This article studies the $l_1$ exact G-penalty function method to solve a multi-dimensional control optimization problem with non-linear dynamical system involving G-convex functionals. Particularly, the exact G-penalized unconstrained problem associated with the aforementioned problem is constructed using the exact penalty approach. Further, the equivalence relation between an optimal solution of the constrained problem and the minimizer of its related unconstrained problem is established imposing the suitable assumptions on the involved functionals. In addition, several numerical examples are formulated to better illustrate the main results, and an informative algorithm is also constructed to specify the certain steps of the solution procedure.

Keywords:

• G-convex functional
• G-optimality conditions
• $l_1$ exact G-penalty function method
• multi-dimensional control optimisation problem

Mathematics subject classification (2020):

• 26B25
• 49J20
• 90C30

Disclosure statement

No potential conflict of interest was reported by the author(s).