Distance to ill-posedness for linear inequality systems under block perturbations: convex and infinite-dimensional cases

DOI10.1080/02331934.2011.606624zbMath1258.90091OpenAlexW1971109641MaRDI QIDQ3112494

Marco A. López, F. Javier Toledo, Juan Parra, Maria J. Cánovas

Publication date: 10 January 2012

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2011.606624

zbMATH Keywords

semi-infinite and infinite programmingdistance to ill-posednessblock perturbationsconvex inequality systems

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Convex programming (90C25) Set-valued and variational analysis (49J53) Linear inequalities of matrices (15A39) Semi-infinite programming (90C34)

Related Items (11)

LP relaxations for a class of linear semi-infinite programming problems ⋮ Robust solutions to multi-objective linear programs with uncertain data ⋮ Best approximate solutions of inconsistent linear inequality systems ⋮ An exact formula for radius of robust feasibility of uncertain linear programs ⋮ Radius of Robust Feasibility for Mixed-Integer Problems ⋮ A note on the radius of robust feasibility for uncertain convex programs ⋮ Radius of robust global error bound for piecewise linear inequality systems ⋮ Robust global error bounds for uncertain linear inequality systems with applications ⋮ The radius of robust feasibility of uncertain mathematical programs: a survey and recent developments ⋮ Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs ⋮ Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

Cites Work

• Some perturbation theory for linear programming
• Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems
• On the existence of solutions for linear inequality systems
• On infinite systems of linear inequalities
• On the Stability of the Feasible Set in Optimization Problems
• Stability of systems of linear equations and inequalities: distance to ill-posedness and metric regularity

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