We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard, S.E. Karisch, F. Rendl. QAPLIB — a quadratic assignment problem library. Journal on Global Optimiza...

A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following n-dimensional quadratic minimization problem in constant time, which is independent of n: z∗ = minv∈Rn〈v, Av〉 + n〈v,diag(d)v〉 + n〈b,v〉, where A ∈ Rn×n is a matrix and d, b ∈ R are vectors. Our theoretical analysis specifies the number of samples k(δ, ) such that the approximat...

The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0− 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : R → R, as well the constraint case: minimize p(x) on a semialgebraic set ...

In this paper, we propose a method for optimizing the alignment of a linear combination of kernels. The proposed algorithm is based on the well-known SMO idea : it solves a quadratic optimization problem by analytically solving subproblems. Ill-conditioned Hessian can thus been avoided. Its implementation does not require any optimization toolbox. Finally, we show that solutions obtained with o...

We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Appl...

An innnite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered. We generalize the interior-point techniques of Nesterov-Nemirovsky to this innnite-dimensional situation. The obtained complexity estimates are similar to nite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic cons...

This paper presents the applications of computational intelligence techniques to economic load dispatch problems. The fuel cost equation of a thermal plant is generally expressed as continuous quadratic equation. In real situations the fuel cost equations can be discontinuous. In view of the above, both continuous and discontinuous fuel cost equations are considered in the present paper. First,...

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available...

The question of post-retirement optimal consumption and investment of retirement savings is addressed. This problem has received considerably less attention than that of how to invest for retirement. With the increase in life span and an increase in private pension funds, a retiree has considerable flexibility in both how to consume and how to continue to invest their retirement funds. Our inte...

The paper investigates the problem of fitting protein complexes into electron density maps. They are represented by high-resolution cryoEM density maps converted into overlapping matrices and partly show a structure of a complex. The general purpose is to define positions of all proteins inside it. This problem is known to be NP-hard, since it lays in the field of combinatorial optimization ove...