Modern Multiplier Rules

DOI10.2307/2320250zbMath0454.90067OpenAlexW4249791376WikidataQ56141952 ScholiaQ56141952MaRDI QIDQ3902841

Bruce Pourciau

Publication date: 1980

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2320250

zbMATH Keywords

separation theoremmultiplier rulesKarush-Kuhn-Tucker theoremconstrained nonlinear programmingEuler-Lagrange multiplier ruleCaratheodory multiplier ruleCaratheodory- John multiplier ruleconvex multiplier ruleJohn multiplier rulestrongly differentiable problem functions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Inequalities and extremum problems involving convexity in convex geometry (52A40) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (18)

On the image of a constrained extremum problem and some applications to the existence of a minimum ⋮ The method of Lagrange multipliers for the class of subsmooth mappings ⋮ A short elementary proof of the Lagrange multiplier theorem ⋮ An invitation to optimality conditions through non-smooth analysis ⋮ On the Caratheodory-John multiplier rule ⋮ Multiplier rules and the separation of convex sets ⋮ Positive semidefinite diagonal minus tail forms are sums of squares ⋮ A multiplier rule on a metric space ⋮ Generating Eigenvalue Bounds Using Optimization ⋮ Multiplier rules for weak pareto optimization problems ⋮ A General Lagrange Multipliers Theorem and Related Questions ⋮ A simple and elementary proof of the Karush-Kuhn-Tucker theorem for inequality-constrained optimization ⋮ On the multiplier rules ⋮ Generalized convexity in non-regular programming problems with inequality-type constraints ⋮ Pooled testing for quarantine decisions ⋮ Approximate controllability for the semilinear heat equation involving gradient terms ⋮ Excess versions of the Minkowski and Hölder inequalities ⋮ A generalization of multiplier rules for infinite-dimensional optimization problems

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