<abstract><p>In this manuscript, we consider well-known multi-task learning (MTL) models from the literature for linear regression problems, such as clustered MTL or weakly constrained MTL. We propose novel reformulations of training problem these models, based on mixed-integer quadratic programming (MIQP) techniques. show that our approach allows to drive optimization process up ce...

Given an undirected graph G = (V,E), we consider the graph bisection problem, which consists in partitioning the nodes of G in two disjoined sets with p and n− p nodes respectively such that the total weight of edges crossing between subsets is minimal. We apply QCR to it, a general method, presented in [4], which combines semidefinite programming (SDP) and Mixed Integer Quadratic Programming (...

in this paper, the energy efficient resource allocation in noma-based heterogeneous cellular network(hcn) systems is investigated. since energy consumption and its limitations is one of the important challenges in fifth generation of cellular networks (5g), we propose a resource allocation problem which allocates power and subcarriers to multiple users to achieve the best system energy efficien...

A standard trick in integer programming is to replace each bounded integer-constrained variable with a small number of binary variables, using the bit representation of the given variable. We show that, in the case of mixed-integer quadratic programs (MIQPs), this process can enable one to obtain stronger linear programming relaxations. Moreover, we give a simple sufficient condition under whic...

We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class convex relaxations which are derived via cuts. To construct these cuts, solve separation problem involving matrix inequality special structure that allows use specialized solution algorithms. Our cuts nonconvex, but define feasible set when in...

Abstract Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel most recent use branch-and-cut techniques from programming that are especially tailored context. In this paper, we consider MIQP-QP problems, i.e., models with convex-quadrat...