Dual gauge programs, with applications to quadratic programming and the minimum-norm problem

DOI10.1007/BF02591851zbMath0632.90054OpenAlexW1994229647MaRDI QIDQ3770288

Robert M. Freund

Publication date: 1987

Published in: Mathematical Programming (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02591851

zbMATH Keywords

duality gapgauge functionLagrange dualconvex quadratic programspositively homogeneouspseudonormsnonnegative convex functiongauge duality theoryminimum \(\ell _ p\) norm problem

Mathematics Subject Classification ID

Convex programming (90C25) Quadratic programming (90C20)

Related Items (16)

Duality of nonconvex optimization with positively homogeneous functions ⋮ Applications of optimization methods to robust stability of linear systems ⋮ Delta Minors, Delta Free Clutters, and Entanglement ⋮ Applications of gauge duality in robust principal component analysis and semidefinite programming ⋮ Screening for a reweighted penalized conditional gradient method ⋮ Convex Geometry of the Generalized Matrix-Fractional Function ⋮ Radial duality. I: Foundations ⋮ Radial duality. II: Applications and algorithms ⋮ No-regret dynamics in the Fenchel game: a unified framework for algorithmic convex optimization ⋮ Duality of optimization problems with gauge functions ⋮ Foundations of Gauge and Perspective Duality ⋮ On local coincidence of a convex set and its tangent cone ⋮ Low-Rank Spectral Optimization via Gauge Duality ⋮ On certain optimization problems related to matrix norms ⋮ Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming ⋮ A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes

Cites Work

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• An extension lemma and homogeneous programming
• Duality in quadratic programming
• Duality in Homogeneous Programming
• Fenchel and Lagrange duality are equivalent
• Explicit duality for convex homogeneous programs
• Symmetric Duality for Structured Convex Programs
• Maximal Separation Theorems for Convex Sets
• Convex Analysis
• Blocking and anti-blocking pairs of polyhedra

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