Jean Charles Gilbert The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) $0\leq x\perp(Mx+q)\geq0$ can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations $\min(x,Mx+q)=0$, which is equivalent to the LCP. When $M$ is an $M$-matrix of order~$n$, the algorithm is known to converge in … Read more
The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their problems can have common features that differ from one collection to the other. Libopt brings a unified … Read more
The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their problems can have common features that differ from one collection to the other. Libopt brings a unified … Read more
Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more
We consider an augmented Lagrangian algorithm for minimizing a convex quadratic function subject to linear inequality constraints. Linear optimization is an important particular instance of this problem. We show that, provided the augmentation parameter is large enough, the constraint value converges {\em globally\/} linearly to zero. This property is viewed as a consequence of the … Read more
An algorithm for solving equality constrained optimization problems is proposed. It can deal with nonconvex functions and uses a truncated conjugate algorithm for detecting nonconvexity. The algorithm ensures convergence from remote starting point by using line-search. Numerical experiments are reported, comparing the approach with the one implemented in the trust region codes ETR and Knitro. … Read more
This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data. Citation Rapport de recherche 4179, INRIA, France, 2001 Article Download View Examples of ill-behaved central paths in convex … Read more
This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of … Read more