Related papers: On the existence of Pareto solutions for polynomia…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…
In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…
In multidisciplinary optimization the designer needs to find solution to optimization problems which include a number of usually contradicting criteria. Such a problem is mathematically related to the field of nonlinear vector optimization…
In this article, we propose an algorithm, NESTA-LASSO, for the LASSO problem, i.e., an underdetermined linear least-squares problem with a 1-norm constraint on the solution. We prove under the assumption of the restricted isometry property…
We present a new elementary proof of the existence of the least and the greatest solutions to initial value problems in the conditions of Peano's existence theorem. Our proof is based on a modification of Perron's method which allows us to…
The object of investigation in this paper are vector nonlinear programming problems with cone constraints. We introduce the notion of a Fritz John pseudoinvex cone-constrained vector problem. We prove that a problem with cone constraints is…
In this paper, we propose criteria for unboundedness of the images of set-valued mappings having closed graphs in Euclidean spaces. We focus on mappings whose domains are non-closed or whose values are connected. These criteria allow us to…
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…
Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose…
We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is…
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…
In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective…
Consider the model where we can access a parity function through random uniform labeled examples in the presence of random classification noise. In this paper, we show that approximating the number of relevant variables in the parity…
We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
In alloy design, the search for candidate materials is often framed as an optimization problem, with the goal of identifying Pareto-optimal solutions across multiple objectives. However, Pareto-optimal solutions do not necessarily satisfy…