On the Geometry Phase in Model-Based Algorithms for Derivative-Free Optimization

A numerical study of model-based methods for derivative-free optimization is presented. These methods typically include a geometry phase whose goal is to ensure the adequacy of the interpolation set. The paper studies the performance of an algorithm that dispenses with the geometry phase altogether (and therefore does not attempt to control the position of the … Read more

A Log-Robust Optimization Approach to Portfolio Management

In this paper we present a robust optimization approach to portfolio management under uncertainty that (i) builds upon the well-established Lognormal model for stock prices while addressing its limitations, and (ii) incorporates the imperfect knowledge on the true distribution of the continuously compounded rates of return, i.e., the increments of the logarithm of the stock … Read more

LANCELOt_simple, a simple interface to LANCELOT B

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

Intensity based Three-Dimensional Reconstruction with Nonlinear Optimization

New images of a three-dimensional scene can be generated from known image sequences using lightfields. To get high quality images, it is important to have accurate information about the structure of the scene. In order to optimize this information, we define a residual-function. This function represents the difference between an image, rendered in a known … Read more

A multilevel algorithm for solving the trust-region subproblem

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

An Active-Set Algorithm for Nonlinear Programming Using Parametric Linear Programming

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

The Squared Slacks Transformation in Nonlinear Programming

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. Citation Cahier du GERAD G-2007-62, Aug. 2007 Article Download View The … Read more

A globally convergent trust-region SQP method without a penalty function for nonlinearly constrained optimization

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. Citation Cooperative Research … Read more

A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

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

Nonlinear programming without a penalty function or a filter

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