Related papers: A solution method for arbitrary polyhedral convex …
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…
We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse…
This paper aims at investigating the contractibility of the solution sets for set optimization problems by utilizing strictly quasi cone-convexlikeness, which is an assumption weaker than strictly cone-convexity, strictly…
A new deconvolution algorithm based on orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost…
We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…
Direct search is one of the most popular derivative-free optimization paradigms, that relies on exploring the variable space using polling directions. To analyze and implement direct search, one typically relies on positive spanning sets.…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex {vector} optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP,…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We present two criteria for checking approximate proper efficiency in vector optimization problems with the ordering cone being a nonnegative orthant. Although the criteria can be established by Benson's approach [H.P. Benson, \textit{An…