arXiv subjects

Rodrigo B. Moreira

Publications and source records attributed to Rodrigo B. Moreira.

3 recordsLinked to original sources

arXiv2026

A New Constraint Qualification for Continuous-Time Nonlinear Programming Based on Asymptotic KKT Conditions

The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an appropriate version of the augmented Lagrange method. These tools are of a theoretical nature, yet they possess practical utility in the identification of candidate solutions to continuous-time programming problems. While this type of optimality condition is valid without imposing any constraint qualification, it is not sufficiently robust to generate good candidate solutions. In some cases, solutions satisfying AKKT conditions are not even stationary. In this study, we investigate conditions that effectively refine this set of candidate solutions with the same precision as the classical Karush-Kuhn-Tucker (KKT) conditions. This is achieved by introducing a novel constraint qualification, designated AKKT-regularity. It has been demonstrated that, under AKKT-regularity, each local optimal solution is shown to satisfy the KKT conditions. In addition, it is demonstrated that this constraint qualification is the weakest possible to ensure such a property. Furthermore, sufficient conditions are provided for its applicability.

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arXiv2026

A New Constraint Qualification for Mixed Constrained Optimal Control

In recent developments, a novel set of necessary optimality conditions for mixed constrained optimal control problems, termed the asymptotic weak maximum principle, has been formulated. These novel conditions deviate from the classical ones by virtue of their sequential nature and the fact that they are satisfied regardless of the regularity conditions imposed on the mixed constraints. Furthermore, due to their asymptotic behaviour, these conditions serve as a precise tool for use as stopping criteria in numerical methods of solution. However, it should be noted that, in certain instances, these conditions may not be sufficiently robust to fully characterize optimal solutions, as they can be satisfied by processes that are not extremals. The present study proposes a novel constraint qualification, meticulously developed to address these asymptotic optimality conditions. It is demonstrated that the asymptotic weak maximum principle implies the classical weak maximum principle when the newly proposed constraint qualification is verified. It is further demonstrated that, in the smooth setting, this constraint qualification is the weakest one that possesses such a property. Additionally, this study present sufficient criteria for the validity of the newly proposed constraint qualification.

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arXiv2026

Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming

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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