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Abstract: In this article we provide an exact expression for computing the autocorrelation coefficient and the autocorrelation length of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters and for the 137 instances of the QAPLIB. Our goal is to better characterize the difficulty of this important class of problems to ease the future definition of new optimization methods. Also, the advance that this represents helps to consolidate QAP as an interesting and now better understood problem. [Copyright &y& Elsevier]

We prove a sufficient global optimality condition for the problem of minimizing a quadratic function subject to quadratic equality constraints where the variables are allowed to take values -1 and 1. We extend the condition to quadratic problems with matrix variables and orthonormality constraints, and in particular to the quadratic assignment problem. [ABSTRACT FROM AUTHOR]

In regular optimal-control problems, Pontryagin's maximum principle specifies possible optimal solutions among trajectories of a Hamiltonian system. In this paper, we show how to extend this approach to singular linear-quadratic optimal-control problems that have only "generalized" optimal solutions. We define generalized Hamiltonian flows whose trajectories are distributions (generalized functions). We show that generalized Hamiltonian trajectories correspond to the generalized optimal solutions of the problem and obtain a geometric description of the generalized optimal synthesis for singular linear-quadratic problems. [ABSTRACT FROM AUTHOR]

A primal-dual active set method for quadratic problems with bound constraints is presented. Based on a guess on the active set, a primal dual pair (x, s) is computed that satisfies the first order optimality condition and the complementarity condition. If (x, s) is not, feasible, a new active sat is determined, and the process is iterated. Sufficient conditions for the iterations to stop in a finite number of steps with an optimal solution are provided. Computational experience indicates that this approach often requires only a few (less than 10) iterations to find the optimal solution. [ABSTRACT FROM AUTHOR]