A geometric approach to nonsmooth optimization with sample applications

DOI10.1016/0362-546X(87)90005-8zbMath0632.49009OpenAlexW2033641834MaRDI QIDQ3769492

Thomas W. Reiland

Publication date: 1987

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(87)90005-8

zbMATH Keywords

optimality conditionspseudoconvexitygeometric programmingClarke's generalized gradientmonotropic programming\(L_ 1\)-approximationconical approximations

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions of several variables, generalizations (26B25) Mathematical programming (90C99) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

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Cites Work

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• Advances in geometric programming
• Foundations of optimization
• Fenchel's duality theorem in generalized geometric programming
• Constrained duality via unconstrained duality in generalized geometric programming
• Optimality conditions in generalized geometric programming
• Saddle points and duality in generalized geometric programming
• A MATHEMATICAL AID IN OPTIMIZING ENGINEERING DESIGNS
• A FURTHER MATHEMATICAL AID IN OPTIMIZING ENGINEERING DESIGNS
• Dual Programs and Minimum Cost
• Necessary Conditions in Nonsmooth Optimization
• Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
• Generalized Gradients and Applications
• Geometric Programming
• On optimality conditions in nondifferentiable programming
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Cost Minimization Problems Treated by Geometric Means