Approximating saddle points as equilibria of differential inclusions

Sjur D. Flåm; Adi Ben-Israel

doi:10.1016/0022-247X(89)90221-7

Approximating saddle points as equilibria of differential inclusions

Sjur D. Flåm, Adi Ben-Israel

Rutgers Business School, Management & Information Systems

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Motivated by nonlinear programming we study a process involving continuous adjustments of both primal and dual variables. Nonsmoothness in problem data or simple restrictions on variables make the velocity of the process possibly nonunique. The process obtained is shown to converge locally under strict monotonicity conditions. Examples are given in terms of augmented Lagrangians. The results are believed to provide a basis for the construction of algorithms.

Original language	English (US)
Pages (from-to)	264-277
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	141
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(89)90221-7
State	Published - Jul 1989

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/0022-247X(89)90221-7

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abstract = "Motivated by nonlinear programming we study a process involving continuous adjustments of both primal and dual variables. Nonsmoothness in problem data or simple restrictions on variables make the velocity of the process possibly nonunique. The process obtained is shown to converge locally under strict monotonicity conditions. Examples are given in terms of augmented Lagrangians. The results are believed to provide a basis for the construction of algorithms.",

author = "Fl{\aa}m, {Sjur D.} and Adi Ben-Israel",

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N2 - Motivated by nonlinear programming we study a process involving continuous adjustments of both primal and dual variables. Nonsmoothness in problem data or simple restrictions on variables make the velocity of the process possibly nonunique. The process obtained is shown to converge locally under strict monotonicity conditions. Examples are given in terms of augmented Lagrangians. The results are believed to provide a basis for the construction of algorithms.

AB - Motivated by nonlinear programming we study a process involving continuous adjustments of both primal and dual variables. Nonsmoothness in problem data or simple restrictions on variables make the velocity of the process possibly nonunique. The process obtained is shown to converge locally under strict monotonicity conditions. Examples are given in terms of augmented Lagrangians. The results are believed to provide a basis for the construction of algorithms.

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Approximating saddle points as equilibria of differential inclusions

Abstract

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