In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefiniteness (such as in semidefinite programming).

Operations research, optimization, constraint programming, hybrid solution methods, decision Handbook of Semidefinite, Cone and Polynomial Optimization:. Learning Outcomes. On successful completion of this module, the student should: Have a working knowledge of the techniques employed in a modern constraint. Constraint-based scheduling: applying constraint programming to scheduling Implementati...

This paper revisits the parametric analysis of semidefinite optimization problems with respect to perturbation objective function along a fixed direction. We review notions invariancy set, nonlinearity interval, and transition point optimal partition, we investigate their characterizations. show that set points is finite continuity mapping, on basis Painlevé–Kuratowski convergence, might fail i...

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev’s inequality for scalar random variables. Two semidefinite programming formulations are presented, with a constructive proof based on convex optimization duality and elementary...