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New results on semidefinite bounds for ℓ 1 -constrained nonconvex quadratic optimization

Yong Xia (2013)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we show that the direct semidefinite programming (SDP) bound for the nonconvex quadratic optimization problem over ℓ1 unit ball (QPL1) is equivalent to the optimal d.c. (difference between convex) bound for the standard quadratic programming reformulation of QPL1. Then we disprove a conjecture about the tightness of the direct SDP bound. Finally, as an extension of QPL1, we study the relaxation problem of the sparse principal component analysis, denoted by QPL2L1. We show that the...

Nonmonotone strategy for minimization of quadratics with simple constraints

M. A. Diniz-Ehrhardt, Zdeněk Dostál, M. A. Gomes-Ruggiero, J. M. Martínez, Sandra Augusta Santos (2001)

Applications of Mathematics

An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified...

Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type

Stanislav Sysala (2010)

Applications of Mathematics

A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...

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