Publication

On iterative algorithms for linear least squares problems with bound constraints

Michel Bierlaire
1991
Journal Articles

Abstract

Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed. The first is a modification of a method proposed by Lötstedt, while the two others are characterized by a technique allowing for fast active set changes, resulting in noticeable improvements in the speed with which constraints active at the solution are identified. The numerical efficiency of those algorithms is experimentally studied, with particular emphasis on the dependence on the starting point and the use of preconditioning for ill-conditioned problems.

Official source

https://infoscience.epfl.ch/entities/publication/2f45c13e-b273-4242-bfed-d4deb95a85cb

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Michel Bierlaire
1991
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2f45c13e-b273-4242-bfed-d4deb95a85cb

About this result

Related concepts (32)

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Constraint satisfaction problem

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families.

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Related publications (31)

On iterative algorithms for linear least squares problems with bound constraints

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