Classical Optimality Conditions under Weaker Assumptions
| العنوان: | Classical Optimality Conditions under Weaker Assumptions |
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| المؤلفون: | Simon. Di |
| المصدر: | SIAM Journal on Optimization. 6:178-197 |
| بيانات النشر: | Society for Industrial & Applied Mathematics (SIAM), 1996. |
| سنة النشر: | 1996 |
| مصطلحات موضوعية: | Mathematical optimization, Optimization problem, Feasible region, Pareto principle, Theoretical Computer Science, Constraint (information theory), symbols.namesake, Lagrange multiplier, symbols, Point (geometry), Differentiable function, Minification, Software, Mathematics |
| الوصف: | In this article, an optimization problem that incorporates equality constraints, inequality constraints, and an abstract constraint is considered. We prove the classical optimality conditions (first-order and second-order, necessary, and sufficient) under weaker assumptions: functions involved are continuous around and differentiable at the optimal point instead of continuously differentiable or strictly differentiable and/or twice differentiable. The proof is based on the exact expressions for the contingent cone and the second-order contingent hull to the feasible set established in this article. It is interesting to note that our second-order Lagrange multiplier rule for minimization problems incorporating a more generalized abstract constraint has an improved appearance. Direct applications to “max-type” minimization problems and Pareto optimality are mentioned. |
| تدمد: | 1095-7189 1052-6234 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::af18ce78cc9c92b3c94e029b8b277114 https://doi.org/10.1137/0806010 |
| رقم الأكسشن: | edsair.doi...........af18ce78cc9c92b3c94e029b8b277114 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10957189 10526234 |
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