Critical Multipliers in Semidefinite Programming

Semidefinite Programming

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

Semidefinite Programming

In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear and nonsmooth, but convex, so semidefinite programs are convex optimization problems. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many app...

Boundedness of KKT Multipliers in fractional programming problem using convexificators

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...

Semidefinite programming

Modified alternating direction method of multipliers for convex quadratic semidefinite programming

The dual form of convex quadratic semidefinite programming (CQSDP) problem, with nonnegative constraints on the matrix variable, is a 4-block convex optimization problem. It is known that, the directly extended 4-block alternating direction method of multipliers (ADMM) is very efficient to solve this dual, but its convergence are not guaranteed. In this paper, we reformulate it as a 3-block con...