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Infinite programming and theorems of the alternative
Author(s) -
Montiel López Pablo,
Ruiz Galán Manuel
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5566
Subject(s) - mathematics , convexity , lagrange multiplier , multiplier (economics) , nonlinear programming , karush–kuhn–tucker conditions , semi infinite programming , nonlinear system , inequality , algebra over a field , pure mathematics , mathematical economics , mathematical optimization , mathematical analysis , regular polygon , physics , quantum mechanics , financial economics , economics , macroeconomics , geometry
In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a family of functions satisfying a certain type of weak convexity, the so‐called infsup‐convexity.