New perspective on some classical results in analysis and optimization

DOI10.1080/10556788.2020.1731748zbMath1501.26010OpenAlexW3012382717MaRDI QIDQ5085263

Yuri G. Evtushenko, Olga A. Brezhneva, Alexey A. Tret'yakov

Publication date: 27 June 2022

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2020.1731748

zbMATH Keywords

optimality conditionsimplicit function theoremWeierstrass theoremFermat theoremLusternik theorem

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46) Set-valued and variational analysis (49J53) Implicit function theorems, Jacobians, transformations with several variables (26B10) Implicit function theorems; global Newton methods on manifolds (58C15) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elementary proof of constructive versions of the tangent direction theorem and the implicit function theorem
• The implicit function theorem for maps that are only differentiable: an elementary proof
• A short elementary proof of the Lagrange multiplier theorem
• The implicit and inverse function theorems: easy proofs
• An elementary proof of the Karush–Kuhn–Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints
• An elementary proof of the Lagrange multiplier theorem in normed linear spaces
• Implicit Functions and Solution Mappings
• Optimization and nonsmooth analysis
• The inverse function theorem of Nash and Moser

This page was built for publication: New perspective on some classical results in analysis and optimization