SIAM Review
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems
SIAM Journal on Optimization
Robust portfolio selection problems
Mathematics of Operations Research
Operations Research
Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems
Mathematical Programming: Series A and B
A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints
SIAM Journal on Optimization
A Robust Optimization Approach to Inventory Theory
Operations Research
Selected topics in robust convex optimization
Mathematical Programming: Series A and B
Robust portfolio selection with uncertain exit time using worst-case VaR strategy
Operations Research Letters
Robust solutions of uncertain linear programs
Operations Research Letters
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In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the duality theory for nonconvex quadratic programs (QPs), we reformulate the robust counterpart as a semidefinite program (SDP) and show the equivalence property under mild assumptions. We also apply the same technique to the uncertain second-order cone programs (SOCPs) with "single" (not side-wise) ellipsoidal uncertainty. Then we derive similar results on the reformulation and the equivalence property. In the numerical experiments, we solve some test problems to demonstrate the efficiency of our reformulation approach. Especially, we compare our approach with another recent method based on Hildebrand's Lorentz positivity.