In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed integer problems.

A globally convergent numerical method is developed for a 2-d Coefficient Inverse Problem for a hyperbolic PDE with the backscattering data. An important part of this technique is the quasi-reversibility method. A global convergence theorem is proven via a Carleman estimate. Results of numerical experiments for the problem modeling imaging of plastic land mines are presented.

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...

We establish the existence of global Lipschitz continuous weak entropy solutions to the Cauchy problem for a class of quasilinear wave equations with an external positional force. We prove the consistency and the convergence of uniformly bounded nite{diierence fractional step approximations. Therefore the uniform bound is shown to hold for globally Lipschitz continuous external forces.

 A constrained SOM based on an equal-distortion principle is proposed for producing globally optimal, or near-optimal, vector quantisation. The principle is applied indirectly to control the width of the neighbourhood of the SOM. Little extra computation costs are introduced but improved performance, both in lower distortion and in stable and fast convergence, is achieved.

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported.

SUMMARY Using well{known concepts from the scalar case (cf. Kor94]) we derive globally convergent multigrid methods for the discretized Signorini problem in linear elasticity. Special care has to be taken in case of varying normal directions. The algorithm can be implemented as a multigrid V{cycle with optimal complexity. In numerical experiments we observed similar convergence rates as for lin...

We use the globally convergent framework proposed by Kojima, Noma, and Yoshise to construct an infeasible-interior-point algorithm for monotone nonlinear complemen-tarity problems. Superlinear convergence is attained when the solution is nondegener-ate and also when the problem is linear. Numerical experiments connrm the eecacy of the proposed approach.

A globally convergent algorithm is presented for the solution of a wide class of semi-infinite programming problems. The method is based on the solution of a sequence of equality constrained quadratic programming problems, and usually has a second order convergence rate. Numerical results illustrating the effectiveness of the method are given.