Related papers: On Reduction of Exhausters via a Support Function …
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
We study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that…
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of…
Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction…
Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
A lexicographic maximum of a set $X \subseteq \mathbb{R}^n$ is a vector in $X$ whose smallest component is as large as possible, and subject to that requirement, whose second smallest component is as large as possible, and so on for the…
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…