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Necessary Optimality Conditions for Non-smooth Continuous-Time Problems Using Convexificators | ||
Control and Optimization in Applied Mathematics | ||
دوره 5، شماره 1، فروردین 2020، صفحه 1-13 اصل مقاله (362.43 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.30473/coam.2021.56443.1154 | ||
نویسنده | ||
Ali Ansari Ardali* | ||
Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, P.O. Box. 88186-34141, Iran | ||
چکیده | ||
In this paper, we develop general necessary optimality conditions of the KKT types for non-smooth continuous-time optimization problems with inequality constraints. The primary instrument in our study is the concept of a convexificator. Based on this concept, non-smooth versions of the Mangasarian-Fromovitz constraint qualification are presented. Then, we derive optimality conditions for this problem under weak assumptions. Indeed, the constraint functions and the objective function that exist in this problem are not necessarily differentiable or convex. | ||
کلیدواژهها | ||
Continuous-time problems؛ Optimality conditions؛ Upper semi-regular convexificator؛ Non-smooth analysis | ||
عنوان مقاله [English] | ||
شرایط لازم بهینگی برای مسائل زمان-پیوسته ناهموار با استفاده از محدبکنندهها | ||
نویسندگان [English] | ||
علی انصاری اردلی | ||
ایران، شهرکرد، دانشگاه شهرکرد، دانشکده علوم ریاضی، گروه ریاضی کاربردی،صندوق پستی 88186-34141 | ||
چکیده [English] | ||
در این مطالعه، شرایط لازم بهینگی از نوع کارش-کان-تاکر را برای یک مسالهی بهینهسازی زمان-پیوستهی ناهموار تعمیم میدهیم. ابزار اصلی ما برای بدست آوردن شرایط بهینگی، استفاده از مفهوم محدبکننده است. ما با استفاده از این مفهوم ابتدا توصیف قیدی مانگاساریان-فروموویتز را برای این دسته از مسائل تعمیم میدهیم، سپس شرایط لازم بهینگی را تحت فرضهای ضعیف بدست میآوریم. در واقع در این مقاله، تابع هدف و توابع قیود را ناهموار و غیرمحدب در نظر میگیریم. | ||
کلیدواژهها [English] | ||
مسائل زمان-پیوسته, شرایط بهینگی, محدبکننده نیم-منظم بالایی, آنالیزناهموار | ||
مراجع | ||
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