Finite Codimensionality Method in Infinite-dimensional Optimization Problems
Abstract
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization theory, a condition of finite codimensionality is employed to ensure the existence of nontrivial Lagrange multipliers. As applications, first-order necessary conditions for optimal control problems of some deterministic/stochastic control systems are derived in a unified manner. Compared with the existing constraint qualifications, the finite codimensionality condition, which is equivalent to some suitable {\it a priori} estimates, can offer a more straightforward verification process in these applications.
Cite
@article{arxiv.2102.00652,
title = {Finite Codimensionality Method in Infinite-dimensional Optimization Problems},
author = {Xu Liu and Qi Lü and Haisen Zhang and Xu Zhang},
journal= {arXiv preprint arXiv:2102.00652},
year = {2024}
}