Related papers: Minimizers of Gerstewitz functionals
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…
We present a general procedure to construct examples of convex scalar variational problems which admit a minimizers with large singular sets. The dimension of the set of singularities is maximal and the minimizer has no higher integrability…
The problem of minimizing an integral functional of a vector-valued Lagrangian on a set of admissible arcs with given endpoints is considered. The problem is tackled by embedding it into a set-optimization problem such that the image space…
We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…
We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations.…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving (computationally) expensive multi- and many-objective optimization…
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…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
Beck and Teboulle's FISTA method for finding a minimizer of the sum of two convex functions, one of which has a Lipschitz continuous gradient whereas the other may be nonsmooth, is arguably the most important optimization algorithm of the…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient…
Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in \cite{MPSC1}, we study the convergence of minima, minimizers…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
We study vector-valued functions that minimise the $L^\infty$-norm of their derivatives for prescribed boundary data. We construct a vector-valued, mass minimising $1$-current (i.e., a generalised geodesic) in the domain such that all…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which…
This study reviews popular stochastic gradient-based schemes based on large least-square problems. These schemes, often called optimizers in machine learning, play a crucial role in finding better model parameters. Hence, this study focuses…