Conic Methods for Unconstrained Minimization and Tensor Methods for Nonlinear Equations

R. B. Schnabel
Additional contact information
R. B. Schnabel: University of Colorado, Dept. of Computer Science

A chapter in Mathematical Programming The State of the Art, 1983, pp 417-438 from Springer

Abstract: Abstract Standard methods for nonlinear equations and unconstrained minimization base each iteration on a linear or quadratic model of the objective function, respectively. Recently, methods using two generalizations of the standard models have been proposed for these problems. Conic methods for unconstrained minimization use a model that is the ratio of a quadratic function divided by the square of a linear function. Tensor methods for nonlinear equations augment the standard linear model with a simple second order term. This paper surveys the research to date on methods for unconstrained minimization and nonlinear equations that use conic and tensor models. It begins with a brief summary of the standard methods, so that the paper is essentially selfcontained.

Keywords: Line Search; Conic Model; Conic Function; Secant Method; Unconstrained Minimization (search for similar items in EconPapers)
Date: 1983
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-68874-4_17

Ordering information: This item can be ordered from
http://www.springer.com/9783642688744

DOI: 10.1007/978-3-642-68874-4_17

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().