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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.12751 |
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| _version_ | 1866909038422261760 |
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| author | Monte, Moisés R. C. do Moreira, Rodrigo B. de Oliveira, Valeriano A. |
| author_facet | Monte, Moisés R. C. do Moreira, Rodrigo B. de Oliveira, Valeriano A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming Monte, Moisés R. C. do Moreira, Rodrigo B. de Oliveira, Valeriano A. Optimization and Control 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. |
| title | Asymptotic KKT Conditions for Continuous-Time Nonlinear Programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.12751 |