Related papers: Set optimization - a rather short introduction
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, computational statistics, and computer science. In this paper,…
In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and…
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 is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…