A nonlinear semidefinite optimization relaxation for the worst-case linear optimization under uncertainties

DOI10.1007/s10107-014-0799-4zbMath1327.90106OpenAlexW2015779025MaRDI QIDQ494344

Jiming Peng, Tao Zhu

Publication date: 31 August 2015

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-014-0799-4

zbMATH Keywords

semidefinite optimizationsystemic riskadjustable robust optimizationaffine decision rulesworst-case linear optimization

Mathematics Subject Classification ID

Semidefinite programming (90C22) Minimax problems in mathematical programming (90C47) Nonconvex programming, global optimization (90C26) Linear programming (90C05)

Related Items (6)

Quantifying outcome functions of linear programs: an approach based on interval-valued right-hand sides ⋮ An effective global algorithm for worst-case linear optimization under polyhedral uncertainty ⋮ Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods ⋮ New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation ⋮ An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation ⋮ Complexity Results and Effective Algorithms for Worst-Case Linear Optimization Under Uncertainties

Uses Software

• SDPT3
• GloptiPoly
• CVX

Cites Work

• Unnamed Item
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• Adjustable robust solutions of uncertain linear programs
• Computable representations for convex hulls of low-dimensional quadratic forms
• Robust Convex Optimization
• Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts
• Systemic Risk in Financial Systems
• Theory and Applications of Robust Optimization
• Risk Assessment for Banking Systems
• On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems
• A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization
• Introduction to Stochastic Programming

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