Le problème des signes de Thurstone. Une application de la méthode SEP
Limited memory solution of bound constrained convex quadratic problems arising in video games
We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and a number of ways of solving an equivalent augmented system. Alternative approaches are briefly surveyed, ...
Local quadratic convergence of SQP for elliptic optimal control problems with mixed control-state constraints
Lösungsalgorithmen für quadratische Optimierungsaufgaben mit nicht notwendig konvexer Zielfunktion
Minimal-Energy Clusters of Hard Spheres.
Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics
The numerical solution of granular dynamics problems with Coulomb friction leads to the problem of minimizing a convex quadratic function with semidefinite Hessian subject to a separable conical constraints. In this paper, we are interested in the numerical solution of this problem. We suggest a modification of an active-set optimal quadratic programming algorithm. The number of projection steps is decreased by using a projected Barzilai-Borwein method. In the numerical experiment, we compare our...
Minimization of Extended Quadratic Functions.
New results on semidefinite bounds for -constrained nonconvex quadratic optimization
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...
New unknowns on the midsurface of a Naghdi's shell model.
Newton-Krylov type algorithm for solving nonlinear least squares problems.
Nonlinear mixed zero-one Programming: Practical and Theoretical Aspects
Nonmonotone strategy for minimization of quadratics with simple constraints
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...
Notwendige und hinreichende Bedingungen für (strenge) Konvexität, Pseudokonvexität und (strenge) Quasikonvexität einer quadratischen Funktion bezüglich einer konvexen Menge
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type
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...
On certain classes of variational inequalities and related iterative algorithms.
On computation of C-stationary points for equilibrium problems with linear complementarity constraints via homotopy method
In the paper we consider EPCCs with convex quadratic objective functions and one set of complementarity constraints. For this class of problems we propose a possible generalization of the homotopy method for finding stationary points of MPCCs. We analyze the difficulties which arise from this generalization. Numerical results illustrate the performance for randomly generated test problems.
On -preinvex-type functions.
On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On Orthogonal Linear ...1 Approximation.