Related papers: On the Solution Existence of Nonconvex Quadratic P…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…
We present a novel technical method for analyzing the hidden convex structure embedded in the joint range of a quadratic mapping defined on a Hilbert space. Our approach stands out by relying exclusively on elementary mathematical…
In this paper we propose accelerated gradient descent schemes for convex optimization problems in Hilbert space. We consider inexact oracle case.
The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
Given any finite set of nonnegative integers, there exists a closed convex set whose facial dimension signature coincides with this set of integers, that is, the dimensions of its nonempty faces comprise exactly this set of integers. In…
Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature.…
Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We…
A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the QCQP. Given a QCQP whose convex relaxation is exact, this paper…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We study a special class of non-convex quadratic programs subject to two (possibly indefinite) quadratic constraints when the level sets of the constraint functions are {\it not} arranged {\it alternatively.} It is shown in the paper that…
We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on…