Ill-posedness with respect to the solvability in linear optimization

DOI10.1016/j.laa.2005.11.023zbMath1097.65067OpenAlexW2036661639MaRDI QIDQ2496624

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

Publication date: 20 July 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.11.023

zbMATH Keywords

stabilityperturbationsill-posed problemslinear optimizationill-posednesscondition numbers

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Sensitivity, stability, parametric optimization (90C31) Linear programming (90C05) Semi-infinite programming (90C34)

Related Items (12)

LP relaxations for a class of linear semi-infinite programming problems ⋮ Sufficient conditions for total ill-posedness in linear semi-infinite optimization ⋮ Recent contributions to linear semi-infinite optimization ⋮ Generic primal-dual solvability in continuous linear semi-infinite programming ⋮ Marco A. López, a pioneer of continuous optimization in Spain ⋮ Stability in linear optimization and related topics. A personal tour ⋮ Characterization of total ill-posedness in linear semi-infinite optimization ⋮ Recent contributions to linear semi-infinite optimization: an update ⋮ Stability and Continuity in Robust Optimization ⋮ Error bounds for the inverse feasible set mapping in linear semi-infinite optimization via a sensitivity dual approach ⋮ Primal, dual and primal-dual partitions in continuous linear optimization ⋮ Stability of the primal-dual partition in linear semi-infinite programming

Cites Work

• Some perturbation theory for linear programming
• Recent contributions to linear semi-infinite optimization
• Distance to ill-posedness and the consistency value of linear semi-infinite inequality systems
• Some characterizations and properties of the ``distance to the ill-posedness and the condition measure of a conic linear system
• Stability Theory for Systems of Inequalities. Part I: Linear Systems
• A Characterization of Stability in Linear Programming
• Stable parametric programming^*
• Stability and Well-Posedness in Linear Semi-Infinite Programming
• Stability Theory for Linear Inequality Systems
• Understanding the Geometry of Infeasible Perturbations of a Conic Linear System
• Unifying Condition Numbers for Linear Programming
• Solving strategies and well-posedness in linear semi-infinite programming
• A characterization of ill-posed data instances for convex programming.
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