Weak Local Extrema in Infinite Horizon Optimal Control Problems
Nico Tauchnitz
TL;DR
This paper develops necessary and sufficient optimality conditions for infinite horizon optimal control problems using weak variations, addressing challenges with state constraints and deriving transversality conditions.
Contribution
It introduces a novel approach using weak variations in weighted spaces to establish comprehensive optimality conditions for infinite horizon control problems.
Findings
Derived adjoint equations and variational inequalities
Established transversality and Mangasarian sufficiency conditions
Discussed difficulties with state constraints
Abstract
In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality. The obtained optimality conditions imply several transversality conditions and the validity of Mangasarian type sufficiency conditions. Arising difficulties in the presence of state constraints are discussed.
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Taxonomy
TopicsOptimization and Variational Analysis · Nonlinear Partial Differential Equations · Contact Mechanics and Variational Inequalities