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21
Variational Surface Modeling
 Computer Graphics
, 1992
"... We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handl ..."
Abstract

Cited by 168 (4 self)
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We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handles for direct manipulation. The complexity of the surface's shape may be increased by adding more control points and curves, without apparent limit. Within the constraints imposed by the controls, the shape of the surface is fully determined by one or more simple criteria, such as smoothness. Our method for solving the resulting constrained variational optimization problems rests on a surface representation scheme allowing nonuniform subdivision of Bspline surfaces. Automatic subdivision is used to ensure that constraints are met, and to enforce error bounds. Efficient numerical solutions are obtained by exploiting linearities in the problem formulation and the representation. Keywords: sur...
LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is descr ..."
Abstract

Cited by 75 (11 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
Iterative Linear Algebra for Constrained Optimization
, 2005
"... Each step of an interior point method for nonlinear optimization requires the solution of a symmetric indefinite linear system known as a KKT system, or more generally, a saddle point problem. As the problem size increases, direct methods become prohibitively expensive to use for solving these probl ..."
Abstract

Cited by 5 (2 self)
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Each step of an interior point method for nonlinear optimization requires the solution of a symmetric indefinite linear system known as a KKT system, or more generally, a saddle point problem. As the problem size increases, direct methods become prohibitively expensive to use for solving these problems; this leads to iterative solvers being the only viable alternative. In this thesis we consider iterative methods for solving saddle point systems and show that a projected preconditioned conjugate gradient method can be applied to these indefinite systems. Such a method requires the use of a specific class of preconditioners, (extended) constraint preconditioners, which exactly replicate some parts of the saddle point system that we wish to solve. The standard method for using constraint preconditioners, at least in the optimization community, has been to choose the constraint
Gams/minos: A Solver For LargeScale Nonlinear Optimization Problems
, 2002
"... This document describes the GAMS interface to MINOS which is a general purpose nonlinear programming solver ..."
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Cited by 2 (0 self)
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This document describes the GAMS interface to MINOS which is a general purpose nonlinear programming solver
Symbiosis between Linear Algebra and Optimization
, 1999
"... The efficiency and effectiveness of most optimization algorithms hinges on the numerical linear algebra algorithms that they utilize. Effective linear algebra is crucial to their success, and because of this, optimization applications have motivated fundamental advances in numerical linear algebra. ..."
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Cited by 2 (0 self)
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The efficiency and effectiveness of most optimization algorithms hinges on the numerical linear algebra algorithms that they utilize. Effective linear algebra is crucial to their success, and because of this, optimization applications have motivated fundamental advances in numerical linear algebra. This essay will highlight contributions of numerical linear algebra to optimization, as well as some optimization problems encountered within linear algebra that contribute to a symbiotic relationship. 1 Introduction The work in any continuous optimization algorithm neatly partitions into two pieces: the work in acquiring information through evaluation of the function and perhaps its derivatives, and the overhead involved in generating points approximating an optimal point. More often than not, this second part of the work is dominated by linear algebra, usually in the form of solution of a linear system or least squares problem and updating of matrix information. Thus, members of the optim...
A Penalty Based Simplex Method for Linear Programming
, 1995
"... We give a general description of a new advanced implementation of the simplex method for linear programming. The method "decouples" a notion of the simplex basic solution into two independent entities: a solution and a basis . This generalization makes it possible to incorporate new strategies into ..."
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We give a general description of a new advanced implementation of the simplex method for linear programming. The method "decouples" a notion of the simplex basic solution into two independent entities: a solution and a basis . This generalization makes it possible to incorporate new strategies into the algorithm since the iterates no longer need to be the vertices of the simplex. An advantage of such approach is a possibility of taking steps along directions that are not simplex edges (in principle they can even cross the interior of the feasible set). It is exploited in our new approach to finding the initial solution in which global infeasibility is handled through a dynamically adjusted penalty term. We present several new techniques that have been incorporated into the method. These features include: ffl previously mentioned method for finding an initial solution, ffl an original approximate steepest edge pricing algorithm, ffl dynamic adjustment of the penalty term. The presenc...
Variational Surface Modeling
, 1992
"... We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handl ..."
Abstract
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We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handles for direct manipulation. The complexity of the surface's shape may be increased by adding more control points and curves, without apparent limit. Within the constraints imposed by the controls, the shape of the surface is fully determined by one or more simple criteria, such as smoothness. Our method for solving the resulting constrained variational optimization problems rests on a surface representation scheme allowing nonuniform subdivision of Bspline surfaces. Automatic subdivision is used to ensure that constraints are met, and to enforce error bounds. Efficient numerical solutions are obtained by exploiting linearities in the problem formulation and the representation. Keywords: su...
Gams/minos
"... Contents: ..................................................................................................................................... 1. INTRODUCTION.............................................................................................. 2 2. HOW TO RUN A MODEL WITH GAMS/MINOS..... ..."
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Contents: ..................................................................................................................................... 1. INTRODUCTION.............................................................................................. 2 2. HOW TO RUN A MODEL WITH GAMS/MINOS.......................................... 2 3. OVERVIEW OF GAMS/MINOS ...................................................................... 2 3.1. Linear programming .................................................................................... 3 3.2. Problems with a Nonlinear Objective .......................................................... 4 3.3. Problems with Nonlinear Constraints .......................................................... 6 4. GAMS OPTIONS .............................................................................................. 7 4.1. Options specified through the option statement........................................... 7 4.2. Options specified throu