Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

Motivated by a recent framework for proving global convergence to critical points of nested alternating minimization algorithms, which was proposed for the case of smooth subproblems, we first show here that non-smooth subproblems can also be handled within this framework. Specifically, we present a novel analysis of an optimization scheme that utilizes the FISTA method as a nested algorithm. We establish the global convergence of this nested scheme to critical points of non-convex and non-smooth optimization problems. In addition, we propose a hybrid framework that allows to implement FISTA when applicable, while still maintaining the global convergence result. The power of nested algorithms using FISTA in the non-convex and non-smooth setting is illustrated with some numerical experiments that show their superiority over existing methods.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)1130-1157
عدد الصفحات28
دوريةJournal of Optimization Theory and Applications
مستوى الصوت199
رقم الإصدار3
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - ديسمبر 2023

All Science Journal Classification (ASJC) codes

  • !!Control and Optimization
  • !!Management Science and Operations Research
  • !!Applied Mathematics

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