Results 1  10
of
11
LargeScale ActiveSet BoxConstrained Optimization Method with Spectral Projected Gradients
 Computational Optimization and Applications
, 2001
"... A new activeset method for smooth boxconstrained minimization is introduced. The algorithm combines an unconstrained method, including a new linesearch which aims to add many constraints to the working set at a single iteration, with a recently introduced technique (spectral projected gradien ..."
Abstract

Cited by 62 (10 self)
 Add to MetaCart
A new activeset method for smooth boxconstrained minimization is introduced. The algorithm combines an unconstrained method, including a new linesearch which aims to add many constraints to the working set at a single iteration, with a recently introduced technique (spectral projected gradient) for dropping constraints from the working set. Global convergence is proved. A computer implementation is fully described and a numerical comparison assesses the reliability of the new algorithm. Keywords: Boxconstrained minimization, numerical methods, activeset strategies, Spectral Projected Gradient. 1
Optimizing the Packing of Cylinders into a Rectangular Container: A Nonlinear Approach
, 2003
"... The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision pr ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box de ned by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to nd the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.
On the convergence properties of the projected gradient method for convex optimization
 Comput. Appl. Math
"... Abstract. When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the noncovex case: the whole sequence converges to an optimal solution under the only hypothesis of existence of minimizers (i.e. without a ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
(Show Context)
Abstract. When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the noncovex case: the whole sequence converges to an optimal solution under the only hypothesis of existence of minimizers (i.e. without assuming e.g. boundedness of the level sets). In this paper we look at the projected gradient method for constrained convex minimization. Convergence of the whole sequence to a minimizer assuming only existence of solutions has also been already established for the variant in which the stepsizes are exogenously given and square summable. In this paper, we prove the result for the more standard (and also more efficient) variant, namely the one in which the stepsizes are determined through an Armijo search. Mathematical subject classification: 90C25, 90C30. Key words: projected gradient method, convex optimization, quasiFejér convergence.
Augmented Lagrangian algorithms based on the spectral projected gradient method for solving nonlinear programming problems
"... The Spectral Projected Gradient method (SPG) is an algorithm for largescale boundconstrained optimization introduced recently by Birgin, Martnez and Raydan. It is based on Raydan's unconstrained generalization of the BarzilaiBorwein method for quadratics. The SPG algorithm turned out to be s ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
The Spectral Projected Gradient method (SPG) is an algorithm for largescale boundconstrained optimization introduced recently by Birgin, Martnez and Raydan. It is based on Raydan's unconstrained generalization of the BarzilaiBorwein method for quadratics. The SPG algorithm turned out to be surprisingly eective for solving many largescale minimization problems with box constraints. Therefore, it is natural to test its performance for solving the subproblems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as underlying convexconstraint solver are introduced (ALSPG), and the methods are tested in two sets of problems. First, a meaningful subset of largescale nonlinearly constrained problems of the CUTE collection is solved and compared with the performance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.
Optimization Problems in the Estimation Or Parameters of Thin Films and the Elimination of the Influence of the Substrate
, 2001
"... In a recent paper, the authors introduced a method to estimate optical parameters of thin lms using transmission data. The associated model assumes that the lm is deposited on a completely transparent substrate. It has been observed, however, that small absorption of substrates affect in a nonneglig ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
In a recent paper, the authors introduced a method to estimate optical parameters of thin lms using transmission data. The associated model assumes that the lm is deposited on a completely transparent substrate. It has been observed, however, that small absorption of substrates affect in a nonnegligible way the transmitted energy. The question arises of how reliable is the estimation method to retrieve optical parameters in the presence of substrates of dierent thicknesses and absorption degrees. In this paper, transmission spectra of thin lms deposited on nontransparent substrates are generated and, as a first approximation, the method based on transparent substrates is used to estimate the optical parameters. As expected, the method is good when the absorption of the substrate is very small, but fails when one deals with less transparent substrates. To overcome this drawback, an iterative procedure is introduced, that allows one to approximate the transmittance with transparent substrate, given the transmittance with absorbent substrate. The updated method turns out to be almost as efficient in the case of absorbent substrates as it was in the case of transparent ones.
Affine Puzzle: Realigning Deformed Object Fragments without Correspondences ⋆
"... Abstract. This paper is addressing the problem of realigning broken objects without correspondences. We consider linear transformations between the object fragments and present the method through 2D and 3D affine transformations. The basic idea is to construct and solve a polynomial system of equati ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper is addressing the problem of realigning broken objects without correspondences. We consider linear transformations between the object fragments and present the method through 2D and 3D affine transformations. The basic idea is to construct and solve a polynomial system of equations which provides the unknown parameters of the alignment. We have quantitatively evaluated the proposed algorithm on a large synthetic dataset containing 2D and 3D images. The results show that the method performs well and robust against segmentation errors. We also present experiments on 2D real images as well as on volumetric medical images applied to surgical planning. 1
Minimization Subproblems and Heuristics for an Applied Clustering Problem
, 2001
"... A practical problem that requires the classification of a set of points of R^n using a criterion not sensitive to bounded outliers is studied in this paper. A fixedpoint (kmeans) algorithm is defined that uses an arbitrary distance function. Finite convergence is proved. A robust distance defined ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
A practical problem that requires the classification of a set of points of R^n using a criterion not sensitive to bounded outliers is studied in this paper. A fixedpoint (kmeans) algorithm is defined that uses an arbitrary distance function. Finite convergence is proved. A robust distance defined by Boente, Fraiman and Yohai is selected for applications. Smooth approximations of this distance are defined and suitable heuristics are introduced to enhance the probability of finding global optimizers. A reallife example is presented and commented.
Optimizing the Packing of Cylinders into a Rectangular Container: A Nonlinear Approach
, 2003
"... Abstract The container loading problem has important industrial and commercial applications. Anincrease in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based ona nonlinear decisio ..."
Abstract
 Add to MetaCart
Abstract The container loading problem has important industrial and commercial applications. Anincrease in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based ona nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to beinside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries tofind the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative studywith other methods of the literature is presented and better results are achieved.
Optimizing the Packing of Cylinders into a Rectangular Container: A Nonlinear Approach
, 2003
"... The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision probl ..."
Abstract
 Add to MetaCart
(Show Context)
The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.
Optimizing the Packing of Cylinders into a Rectangular Container: A Nonlinear Approach
, 2003
"... The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision probl ..."
Abstract
 Add to MetaCart
(Show Context)
The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.