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The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning,…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
In the present paper, the Polyak's principle, concerning convexity of the images of small balls through C1,1 mappings, is employed in the study of vector optimization problems. This leads to extend to such a context achievements of local…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in mathematical programming, including…
In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…
Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is…
The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…
Benchmark problems play a central role in assessing the performance of numerical optimization algorithms. However, many existing constrained multiobjective optimization benchmark problems rely on overly restricted constructions or lack…
Many real-world optimization problems can be stated in terms of submodular functions. Furthermore, these real-world problems often involve uncertainties which may lead to the violation of given constraints. A lot of evolutionary…
In this paper we consider well-posedness properties of vector optimization problems with objective function $f: X \to Y$ where $X$ and $Y$ are Banach spaces and $Y$ is partially ordered by a closed convex pointed cone with nonempty…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by…
We present a method to design parallel algorithms for constrained combinatorial optimization problems. Our method solves and generalizes many classical combinatorial optimization problems including the stable marriage problem, the shortest…
In this paper, we propose a simple global optimisation algorithm inspired by Pareto's principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of…
We consider a Ramsey model with several households with heterogeneous preferences who are able to borrow capital to each other. Since the capital constraints of one household then depends on the others' capital, one can no longer optimize…