Related papers: Set optimization - a rather short introduction
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
This paper reviews recent advances in big data optimization, providing the state-of-art of this emerging field. The main focus in this review are optimization techniques being applied in big data analysis environments. Integer linear…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…