Quadratic assignment problems (QAPs) and quadratic assignment matchings (QAMs) recently gained a lot of interest in computer graphics and vision, e.g. for shape and graph matching. Literature describes several convex relaxations to approximate solutions of the NP-hard QAPs in polynomial time. We compare the convex relaxations recently introduced in computer graphics and vision to established ap...

The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J.B. Lasserre. Convexity in semialgebraic geometry and polynomial optimization. SIAM J. Optim. 19, 1995–2014, 2009.] We give a new proof of the finite convergence property, that does not require the assumption that the Hessian of the...

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite ...

This survey contains recent developments for computing verified results of convex constrained optimization problems, with emphasis on applications. Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming. A discussion of important problem transforma...

This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing semidefinite and quadratic programming relaxations and dominate existing cuts proposed in the literature. Combined with model intersection and bound tightening, the new l...

Several types of relaxations for binary quadratic polynomial programs can be obtained using linear, secondorder cone, or semidefinite techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our framework, we re-derive previous relaxation schemes and provide new ones. In particular, w...

We consider the outer approximation problem of finding a minimum radius ball enclosing a given intersection of at most n− 1 balls in R. We show that if the aforementioned intersection has a nonempty interior, then the problem reduces to minimizing a convex quadratic function over the unit simplex. This result is established by using convexity and representation theorems for a class of quadratic...

A robust beamforming with quadratic constraints, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With this formulation, the constraints on magnitude response can be easily imposed on the adaptive beamformer. And the non-convex quadratic constraints can be transformed into linear constraints. Therefore, the proposed method can be robust against the steering dir...