Szeretettel meghívjuk Mirjam Dür előadására
az Optimalizálási Szeminárium keretében
2019. november 21-én csütörtökön 14:15 - 15:45
Helyszín: BME H. épület 405/a terem
Mirjam Dür - University of Augsburg
Copositive optimization and completely positive matrix factorization
A copositive optimization problem is a problem in matrix variables with a constraint which requires that the matrix be in the cone of copositive matrices. Its dual cone which appears in the dual optimization problem is the cone of completely positive matrices. These cones have received considerable attention because it has turned out that many nonconvex quadratic optimization problems as well as combinatorial problems can be formulated as linear problems over these cones. This is remarkable since by this approach, a nonconvex optimization problem is reformulated equivalently as a convex problem. The complexity of the original problem is entirely shifted into the cone constraint
When trying to recover the solution of the underlying problem from the optimal matrix solution, it is necessary to be able to factorize a given completely positive matrix X* as X*=∑i (xi xiT) with xi ϵ ℝn, xi > 0 for all i. The talk will introduce a method to solve this factorization problem: we reformulate the factorization problem as a nonconvex feasibility problem and develop a solution method based on alternating projections. A local convergence result can be shown for this algorithm, and numerical experiments show that the algorithm performs very well in practice.