We describe LANCELOT_simple, an interface to the LANCELOT B nonlinear optimization package within the GALAHAD} library (Gould, Orban, Toint, 2003) which ignores problem structure. The result is an easy-to-use Fortran 90 subroutine, with a small number of intuitively interpretable arguments. However, since structure is ignored, the means of presenting problems to the solver limited and … Read more
We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest … Read more
This paper describes an active-set algorithm for nonlinear programming that solves a parametric linear programming subproblem at each iteration to generate an estimate of the active set. A step is then computed by solving an equality constrained quadratic program based on this active-set estimate. This approach respresents an extension of the standard sequential linear-quadratic programming … Read more
We recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. Numerical examples performed with the sequential quadratic programming method illustrate those reasons. CitationCahier du GERAD G-2007-62, Aug. 2007ArticleDownload View PDF
In this paper, we propose a new trust-region SQP method, which uses no penalty function, for solving nonlinearly constrained optimization problem. Our method consists of alternate two phases. Specifically, we alternately proceed the feasibility restoration phase and the objective function minimization phase. The global convergence property of the proposed method is shown. CitationCooperative Research Report … Read more
A recursive trust-region method is introduced for the solution of bound-constrained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the … Read more
A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, … Read more
In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, … Read more
We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative … Read more
Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function’s local curvature is incomplete, in the sense that it may be restricted to a fixed set of “test directions” and may not be available at every iteration. It is shown that convergence to local “weak” … Read more