Norm duality for convex processes and applications

DOI10.1007/BF00938589zbMath0557.49009OpenAlexW99853481WikidataQ56935997 ScholiaQ56935997MaRDI QIDQ762453

Jonathan M. Borwein

Publication date: 1986

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00938589

zbMATH Keywords

boundednessBanach spacesurjectivityconvex processinequality systemsnorm duality

Mathematics Subject Classification ID

Convex programming (90C25) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Inequalities and extremum problems involving convexity in convex geometry (52A40) Duality theory (optimization) (49N15) Duality and reflexivity in normed linear and Banach spaces (46B10) Optimality conditions for problems in abstract spaces (49K27)

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Cites Work

• Generalized linear complementarity problems treated without fixed-point theory
• On the existence and nonexistence of Lagrange multipliers in Banach spaces
• Another application of Guignard's generalized Kuhn-Tucker conditions
• A generalization of the Farkas lemma and applications to convex programming
• Ordered linear spaces
• Adjoint Process Duality
• Remark on the Constraint Sets in Linear Programming
• Regularity and Stability for Convex Multivalued Functions
• A Lagrange multiplier theorem and a sandwich theorem for convex relations.
• A generalized Farkas lemma with applications to quasidifferentiable programming
• The Open Mapping Theorem
• Weak Tangent Cones and Optimization in a Banach Space
• Monotone processes of convex and concave type
• Normed Convex Processes
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