Tackling optimization in mixed domains (continuous and discrete decision variables) has recently gained attention, causing the development of various extensions of continuous optimization algorithms. In order to more ...
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We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical Cr performance function has a unique maximizing m...
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We consider a large-scale convex program with functional constraints, where interior point methods are intractable due to the problem size. The effective solution techniques for these problems permit only simple opera...
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We consider a large-scale convex program with functional constraints, where interior point methods are intractable due to the problem size. The effective solution techniques for these problems permit only simple operations at each iteration, and thus are based on primal-dual first-order methods such as the Arrow-Hurwicz-Uzawa subgradient method, which utilize only gradient computations and projections at each iteration. Such primal-dual algorithms admit the interpretation of solving the associated saddle point problem arising from the Lagrange dual. We revisit these methods through the lens of regret minimization from online learning and present a flexible framework. While it is well known that two regret-minimizing algorithms can be used to solve a convex-concave saddle point problem at the standard rate of O (1/root T), our framework for primal-dual algorithms allows us to exploit structural properties such as smoothness and/or strong convexity and achieve better convergence rates in favorable cases. In particular, for non-smooth problems with strongly convex objectives, our primal-dual framework equipped with an appropriate modification of Nesterov's dual averaging algorithm achieves O (1/T) convergence rate.
作者：
Henke, DorotheeLefebvre, HenriSchmidt, MartinThürauf, JohannesUniversity of Passau
School of Business Economics and Information Systems Chair of Business Decisions and Data Science Dr.-Hans-Kapfinger-Str. 30 Passau94032 Germany Trier University
Department of Mathematics Universitätsring 15 Trier54296 Germany
Department Liberal Arts and Social Sciences Discrete Optimization Lab Dr.-Luise-Herzberg-Str. 4 Nuremberg90461 Germany
The literature on pessimistic bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling co...
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In next basket recommendation (NBR) a set of items is recommended to users based on their historical basket sequences. In many domains, the recommended baskets consist of both repeat items and explore items. Some stat...
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In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it ...
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Researchers have explored methods to maximize energy output from PV systems, with tilt and azimuth optimization being a significant area of focus. While some studies have proposed standard guidelines for tilt and azim...
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