{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:53:23Z","timestamp":1760230403083,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico, DGAPA-UNAM","award":["PAPIIT-IN102220"],"award-info":[{"award-number":["PAPIIT-IN102220"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For optimal control problems of Bolza involving time-state-control mixed constraints, containing inequalities and equalities, fixed initial end-point, variable final end-point, and nonlinear dynamics, sufficient conditions for weak minima are derived. The proposed algorithm allows us to avoid hypotheses such as the continuity of the second derivatives of the functions delimiting the problems, the continuity of the optimal controls or the parametrization of the final variable end-point. We also present a relaxation relative to some similar works, in the sense that we arrive essentially to the same conclusions but making weaker assumptions.<\/jats:p>","DOI":"10.3390\/sym14081520","type":"journal-article","created":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:17:27Z","timestamp":1658794647000},"page":"1520","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sufficiency for Weak Minima in Optimal Control Subject to Mixed Constraints"],"prefix":"10.3390","volume":"14","author":[{"given":"Gerardo S\u00e1nchez","family":"Licea","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1070\/IM1987v028n02ABEH000882","article-title":"Quadratic conditions for the Pontryagin minimum in an optimal control problem linear with respect to the control. 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