# روشی برای تعیین مجموعه جواب‌های مسائل بهینه‌سازی غیرمحدب از طریق مسئله‌ی دوگان متناظرشان

نوع مقاله: مقاله پژوهشی

نویسنده

گروه ریاضی، دانشگاه اصفهان، اصفهان، ایران.

10.22105/dmor.2019.189959.1123

چکیده

دراین مقاله، روشی برای تعیین مجموعه‌جواب‌های کلاسی از مسائل بهینه‌سازی غیرمحدب را از طریق مسئله‌ی دوگان متناظرشان ارائه می‌دهیم. درواقع مسئله‌ی بهینه‌سازی مقیدی که درنظر می‌گیریم دارای توابع محدب‌نما و موضعاً لیپ‌شیتز هستند که لزومامحدب و هموار نیستند و دسته‌ی وسیعی از توابع غیرمحدب غیرهموار را شامل می‌شوند. در روش پیشنهادی برای مشخصه‌سازی مجموعه‌جواب‌های مسئله‌ی اولیه، یک مسئله‌ی دوگان فرمول‌بندی می‌شود که ترکیبی‌از نوع ولف و نوع موند-ویر می‌باشد. در ‌ابتدا برخی‌از ویژگی‌های تابع لاگرانژی متناظر‌با این مسائل را بررسی و سپس اثبات مشخصه‌سازی مجموعه‌جواب‌های آن‌ها را بیان خواهیم کرد.

کلیدواژه‌ها

عنوان مقاله [English]

### A method for characterizing the solution set of nonconvex optimization problems via their dual problems

نویسنده [English]

Department of Mathematics, University of Isfahan, Isfahan, Iran.
چکیده [English]

In this paper, we present a method for charaterizing the solution set of nonconvex optimization problems via their dual problems. In fact, the constrainted optimization problem which is considerd has pseudoconvex and locally Lipschitz functions, which are not necessarily convex and smooth, and include a wide class of non-convex non-smooth functions. In the proposed method, a dual problem is formulated to characterizations of the solution set of the primal problem in a mixed type of Wolfe type and Mond-Weir type. First, we introduce some of the properties of the Lagrangian functions associated to these problems and then we explain the proof of the characterization of their solution sets.

کلیدواژه‌ها [English]

• duality
• Lagrangian function
• Solution set
• non-convex optimization

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### سابقه مقاله

• تاریخ دریافت: 23 خرداد 1398
• تاریخ بازنگری: 02 شهریور 1398
• تاریخ پذیرش: 02 آبان 1398