Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
On the robust shortest path problem
Computers and Operations Research
Mathematics of Operations Research
Robust portfolio selection problems
Mathematics of Operations Research
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Tractable Approximations to Robust Conic Optimization Problems
Mathematical Programming: Series A and B
Ambiguous chance constrained problems and robust optimization
Mathematical Programming: Series A and B
Robust solutions of uncertain linear programs
Operations Research Letters
On the complexity of the robust spanning tree problem with interval data
Operations Research Letters
The robust spanning tree problem with interval data
Operations Research Letters
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Three measures of robustness (absolute robustness, deviation robustness and relative robustness), whose choice depends on the goals of the decision maker, have been proposed for uncertain optimization problems. Absolute robustness has been thoroughly studied, whereas the others have been studied to less of a degree.We focus on deviation robustness for uncertain convex quadratic programming problems with ellipsoidal uncertainties and propose a relaxation technique based on random sampling for robust deviation optimization problems. We theoretically and experimentally show that solving the relaxation problem gives a tighter lower bound than solving a simple sampled relaxation problem. Furthermore, we measure the robustness of the solution in a probabilistic setting. The number of random samples is estimated for obtaining an approximate solution with a probabilistic guarantee, and the approximation error is evaluated a-priori and a-posteriori. Our relaxation algorithm with a probabilistic guarantee utilizes a-posteriori assessment to evaluate the accuracy of the approximate solutions.