This paper deals with several combinatorial optimization problems. The most challenging such problem is the quadratic assignment problem. It is considered in both two dimensions (QAP) and in three dimensions (Q3AP) and in the context of communication engineering. Semidefinite relaxations are used to derive lower bounds for the optimum while heuristics are applied to either find upper bounds or ...

Semidefinite programs are an important class of convex optimization problems. It can be solved efficiently by SDP solvers in Matlab, such as SeDuMi, SDPT3, DSDP. However, since we are running fixed precision SDP solvers in Matlab, for some applications, due to the numerical error, we can not get good results. SDPTools is a Maple package to solve SDP in high precision. We apply SDPTools to the c...

This contribution presents a kinetic model identification scheme that guarantees convergence to global optimality. The use of the extent-based incremental approach allows one to (i) identify each reaction individually, and (ii) reduce the number of parameters to identify via optimization to the ones that appear nonlinearly in the investigated rate law. Via Taylor expansion, the identification p...

Many machine learning tasks (e.g. metric and manifold learning problems) can be formulated as convex semidefinite programs. To enable the application of these tasks on a large-scale, scalability and computational efficiency are considered desirable properties for a practical semidefinite programming algorithm. In this paper, we theoretically analyse a new bilateral greedy optimization(denoted B...

In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstractio...

A convex semidefinite programming problem is a convex constrained optimization problem, where the constraints are linear matrix inequalities, for which the standard Lagrangian condition is sufficient for optimality. However, this condition requires constraint qualifications to completely characterize optimality. We present a necessary and sufficient condition for optimality without a constraint...

We propose a merit function for the expected contrast to noise ratio in tissue quantifications, and formulate a nonlinear, nonconvex semidefinite optimization problem to select locally-optimal balanced steady-state free precession (bSSFP) pulse-sequence design variables. The method could be applied to other pulse sequence types, arbitrary numbers of tissues, and numbers of images. To solve the ...

A spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one. This approach comes from applying a moment relaxation to a suitable polynomial optimization formulation. The hierarchical criterion is stronger ...

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...

This paper presents generalizations of semidefinite programming formulations of 1norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless compressed sensing, and other applications in signal processing. Results related to the generalized Kalman–Yakubovich–Popov lemma in linear system theory provide simpl...