We study certain linear and semidefinite programming lifting approximation schemes for
computing the stability number of a graph. Our work is based on and refines de Klerk and …

We study two-stage adjustable robust linear programming in which the right-hand sides are
uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the …

We consider the problem of computing the minimum value pmin taken by a polynomial p (x)
of degree d over the standard simplex Δ. This is an NP-hard problem already for degree d …

Polynomial optimization encompasses a very rich class of problems in which both the
objective and constraints can be written in terms of polynomials on the decision variables …

We show that any (nonconvex) quadratically constrained quadratic program (QCQP) can be
represented as a generalized copositive program. In fact, we provide two representations …

Copositive optimization is a quickly expanding scientific research domain with wide-spread
applications ranging from global nonconvex problems in engineering to NP-hard …

The elegant theoretical results for strong duality and strict complementarity for linear
programming, LP, lie behind the success of current algorithms. In addition, preprocessing is …

To find a global optimal solution to the quadratically constrained quadratic programming
problem, we explore the relationship between its Lagrangian multipliers and related linear …

The success of the convex-concave procedure (CCCP), a widely used technique for non-
convex optimization, crucially depends on finding a decomposition of the objective function …

We investigate the hierarchy of conic inner approximations K n (r)(r∈ N) for the copositive
cone COP n, introduced by Parrilo (2000)[22]. It is known that COP 4= K 4 (0) and that, while …