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This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…

Optimization and Control · Mathematics 2025-02-27 Rajmadan Lakshmanan , Alois Pichler , Miloš Kopa

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…

Optimization and Control · Mathematics 2021-01-14 Dmitry Pasechnyuk , Anton Anikin , Vladislav Matyukhin

We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…

Data Structures and Algorithms · Computer Science 2025-11-18 Niv Buchbinder , Joseph , Naor , David Wajc

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Optimization and Control · Mathematics 2023-07-13 Maria-Luiza Vladarean , Nikita Doikov , Martin Jaggi , Nicolas Flammarion

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

Optimization and Control · Mathematics 2019-02-06 Yi Xu , Zhuoning Yuan , Sen Yang , Rong Jin , Tianbao Yang

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…

Optimization and Control · Mathematics 2016-12-02 Giovanni P. Crespi , Andreas H. Hamel , Carola Schrage

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

Information Theory · Computer Science 2012-03-22 Amir Beck , Yonina C. Eldar

Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…

Optimization and Control · Mathematics 2016-12-02 Giovanni P. Crespi , Carola Schrage

Non-convex optimization problems are challenging to solve; the success and computational expense of a gradient descent algorithm or variant depend heavily on the initialization strategy. Often, either random initialization is used or…

Machine Learning · Computer Science 2020-12-23 Kartik Ahuja , Amit Dhurandhar , Kush R. Varshney

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a…

Optimization and Control · Mathematics 2021-06-23 Julien Keutchayan , Janosch Ortmann , Walter Rei

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Optimization and Control · Mathematics 2019-12-12 Jelena Diakonikolas , Lorenzo Orecchia

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…

Optimization and Control · Mathematics 2024-10-14 Jamie Fairbrother , Marc Goerigk , Mohammad Khosravi

Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision…

Machine Learning · Computer Science 2022-06-09 Fan Yang , Kai He , Linxiao Yang , Hongxia Du , Jingbang Yang , Bo Yang , Liang Sun

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

Optimization and Control · Mathematics 2025-01-20 Yuhao Wang , Seong-Hee Kim , Enlu Zhou

We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…

Optimization and Control · Mathematics 2024-01-10 Gabriele Iommazzo , Claudia D'Ambrosio , Antonio Frangioni , Leo Liberti

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…

Machine Learning · Computer Science 2017-11-07 Mohammad Reza Karimi , Mario Lucic , Hamed Hassani , Andreas Krause

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Quantum Physics · Physics 2018-08-20 Patrick Rebentrost , Maria Schuld , Leonard Wossnig , Francesco Petruccione , Seth Lloyd

Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes…

Data Structures and Algorithms · Computer Science 2019-05-22 Simon Bruggmann , Rico Zenklusen

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Optimization and Control · Mathematics 2011-07-01 Qihang Lin , Xi Chen , Javier Pena