Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

Bandpass delta sigma optimization using parameter identification

International audienceIn this paper, a new method to optimize the noise shape of a bandpass delta sigma (BPDS) modulator for a digital transmitter is presented. The optimal coefficients of BPDS structure are obtained by minimization of a quadratic criterion based on prediction error. To demonstrate the effectiveness of this approach, simulated results for a 6th order BPDS structure are presented

ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS

In this paper, a new iterative method  for solving  convex minimization  problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization  problems involving bounded linear operator. Our theorems are significant improvements on several important recent results