This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the implemented algorithm, the syntax and calling sequences, a simple numerical example and some more advanced features. The implemented method consists in solving the...

Yuan’s theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we provide a tractable extension of Yuan’s theorem of the alternative to the symmetric tensor setting. As an application, we establish that the optimal value of...

A positively invariant set is an important concept in dynamical systems. The study of conditions for discrete-time systems one interesting topic both theoretical studies and practical applications research. Different methods characterizing the invariance different types sets have been established. For example, ellipsoidal Lorenz cone, which are quadratic convex sets, properties from a polyhedra...

Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, i.e., a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper, we focus on general inner approximations of the cone of completely positive matrices on instances ...

In this paper, we show a method for finding all extremal rays of polyhedral convex cones with some complementarity conditions. The polyhedral convex cone is defined as the intersection of half-spaces expressed by linear inequalities. By a complementarity extremal ray, we mean an extremal ray vector that satisfies some complementarity conditions among its elen~nts. Our method is iterative in the...

For a symmetric positive semidefinite linear system of equations Qx = b, where x = (x1, . . . , xs) is partitioned into s blocks, with s ≥ 2, we show that each cycle of the classical block symmetric Gauss-Seidel (block sGS) method exactly solves the associated quadratic programming (QP) problem but added with an extra proximal term of the form 12‖x−x ‖T , where T is a symmetric positive semidef...

Multi objective quadratic fractional programming (MOQFP) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the objecti...