A general theory of dual optimization problems

DOI10.1016/0022-247X(86)90046-6zbMath0598.49011MaRDI QIDQ1079800

Ivan Singer

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Lagrangian dualcoupling functionalsLagrangian functionalsperturbation functionalsperturbational dualSurrogate dualunified theory of dual optimization

Mathematics Subject Classification ID

Nonlinear programming (90C30) Methods involving semicontinuity and convergence; relaxation (49J45) Duality theory (optimization) (49N15)

Related Items (19)

Jets, generalised convexity, proximal normality and differences of functions ⋮ Abstract subdifferentials and some characterizations of optimal solutions ⋮ Some further relations between unperturbational and perturbational dual optimization problems ⋮ Some characterizations of φ-Lagrangian dual problems ⋮ Diewert-Crouzeix conjugation for general quasiconvex duality and applications ⋮ Fenchel conjugate via Busemann function on Hadamard manifolds ⋮ Some characterizations of surrogate dual problems ⋮ Optimization by level set methods vi:generalizations of surrogate type reverse convex duality ⋮ DC programming: overview. ⋮ On the duality of a non-convex optimization problem and the strong unicity constant in linear Chebyshev approximation ⋮ Quasiconvex duality theory by generalized conjugation methods ⋮ Nonlinear Lagrangian theory for nonconvex optimization. ⋮ Dualities between complete lattices ⋮ On duality for Boolean programming ⋮ Some general Lagrangian duality theorems ⋮ Optimality conditions and duality for DC programming in locally convex spaces ⋮ A general theory of dual optimization problems. II: On the perturbational dual problem corresponding to an unperturbational dual problem ⋮ Some characterizations of perturbational dual problems ⋮ Quasiconjugates of functions, duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint, and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Surrogate dual problems and surrogate Lagrangians
• Some relations between dualities, polarities, coupling functionals, and conjugations
• A general theory of surrogate dual and perturbational extended surrogate dual optimization problems
• Abstract study of optimality conditions
• Duality theorems for linear systems and convex systems
• Duality theorems for perturbed convex optimization
• Generalizations of methods of best approximation to convex optimization in locally convex spaces. II: hyperbolic theorems
• Inf-convolution, sous-additivite, convexite des fonctions numériques
• Surrogate conjugate functionals and surrogate convexity
• DUALITY, HAAR PROGRAMS, AND FINITE SEQUENCE SPACES
• The lower semi-continuous quasi-convex hull as a normalized second conjugate
• Optimization by level set methods v:duality theorems for perturbed optimization problems²
• Dualität bei diskreten steuerungsproblemen
• Some new applications of the Fenchel-Rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation
• An elementary survey of general duality theory in mathematical programming
• Optimization by level set methods. IV: Generalizations and complements
• On $\Phi $-Convexity in Extremal Problems
• A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem
• Extensions of Lagrange Multipliers in Nonlinear Programming
• Quasi-Convex Programming
• Surrogate Mathematical Programming

This page was built for publication: A general theory of dual optimization problems