Equivalence of saddle-points and optima for non-concave programmes
type: Item
instance of: scholarly article
title: Equivalence of saddle-points and optima for non-concave programmes
zbMATH Open document ID: 0571.90078
DOI: 10.1016/0196-8858(84)90015-0
author: Geoffrey Heal
published in: Advances in Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A basic result of optimization theory is that a saddle-point of the Lagrangian is an optimum of the associated programming problem, independently of any concavity assumptions. It is also well known that under concavity assumptions the two are equivalent; i.e. an optimum is always a saddle-point. It is demonstrated that this basic equivalence of saddle-points and optima in fact holds for a much larger class of problems, which are not necessarily concave, but are equivalent to concave programmes up to a diffeomorphism. This class generalizes the class of geometric programmes.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 3912123
zbMATH Keywords: saddle-point
zbMATH Keywords: Lagrangian
zbMATH Keywords: equivalence of saddle-points and optima
MaRDI profile type: Publication
full work available at URL: 0196-8858(84)90015-0
OpenAlex ID: W2073732133
cites work: Stability of the Gradient Process in n-Person Games
cites work: Constraint qualifications in maximization problems
cites work: Q3266142
cites work: Q4135211
cites work: On generalized means and generalized convex functions
cites work: Equity, Efficiency and Increasing Returns
cites work: Intersecting families of sets and the topology of cones in economics
cites work: The geometry of implementation: a necessary and sufficient condition for straightforward games
cites work: Q4161112
cites work: External Economies of Scale and Competitive Equilibrium
cites work: Q3942750
cites work: Q5557595
cites work: Q4770704
cites work: Stationary Ordinal Utility and Impatience
cites work: Contractibility and Convexity
cites work: Morse Theory. (AM-51)
cites work: Q3890433
cites work: An existence theorem for the core of a productive economy with increasing returns
cites work: Q3952705
cites work: The Generic Nature of Optimality Conditions in Nonlinear Programming
cites work: Uniqueness conditions for Kuhn-Tucker points on a disk
cites work: On functions whose stationary points are global minima
description: scientific article; zbMATH DE number 3912123