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arXiv · 2605.12751

Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming

Moisés R. C. do Monte·Rodrigo B. Moreira·Valeriano A. de Oliveira
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Abstract

This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of solutions converging to the optimal solution is demonstrated to exist, and such that Karush-Kuhn-Tucker-type conditions are satisfied asymptotically. It is shown that these sequential Karush-Kuhn-Tucker-type conditions also become sufficient for optimality under convexity assumptions. Sequential optimality conditions are a valuable tool for determining when to terminate a numerical method of solution. In this regard, an augmented Lagrangian-type method is proposed for numerically solving continuous-time programming problems. A convergence analysis concerning viability and optimality is presented. The performance of the method is evaluated by applying it to solve instances of continuous-time problems found in the literature.

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Moisés R. C. do Monte, Rodrigo B. Moreira, Valeriano A. de Oliveira. 2026-05-12. Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming. https://arxiv.org/abs/2605.12751

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