In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification.

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

Format (5.1.1) covers all uncertain optimization problems considered so far; moreover, in these latter problems the objective f and the right hand side F of the constraints always were bi-affine in x, ζ, (that is, affine in x when ζ is fixed, and affine in ζ, x being fixed), and K was a “simple” convex cone (a direct product of nonnegative rays/Lorentz cones/Semidefinite cones, depending on whe...

We propose methods to solve time-varying, sensor and actuator (SaA) selection problems for uncertain cyberphysical systems. We show that many SaA selection problems for optimizing a variety of control and estimation metrics can be posed as semidefinite optimization problems with mixed-integer bilinear matrix inequalities (MIBMIs). Although this class of optimization problems is computationally ...

Minimizing a polynomial function over a region defined by polynomial inequalities mod4 els broad classes of hard problems from combinatorics, geometry and optimization. New algorithmic 5 approaches have emerged recently for computing the global minimum, by combining tools from real 6 algebra (sums of squares of polynomials) and functional analysis (moments of measures) with semidef7 inite optim...

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been two dominant algorithmic approaches to this problem: Greedy methods called the matching pursuit (MP) and the linear programming based approaches called the ba...

A polynomial SDP (semidefinite program) minimizes a polynomial objective function over a feasible region described by a positive semidefinite constraint of a symmetric matrix whose components are multivariate polynomials. Sums of squares relaxations developed for polynomial optimization problems are extended to propose sums of squares relaxations for polynomial SDPs with an additional constrain...

In this paper, Conic optimization and semidefinite programming (SDP) are utilized and applied in classification problem. Two new classification algorithms are proposed and completely described. The new algorithms are; the Voting Classifier (VC) and the N-ellipsoidal Classifier (NEC). Both are built on solving a Semidefinite Quadratic Linear (SQL) optimization problem of dimension n where n is t...

We show that SDP (semidefinite programming) and SOCP (second order cone programming) relaxations provide exact optimal solutions for a class of nonconvex quadratic optimization problems. It is a generalization of the results by S. Zhang for a subclass of quadratic maximization problems that have nonnegative off-diagonal coefficient matrices of objective quadratic functions and diagonal coeffici...

Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from Rn×k, then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower ...