Geometric measures of convex sets and bounds on problem sensitivity and robustness for conic linear optimization

The effect of data perturbation and uncertainty has always been an important consideration in Optimization. It is important to know whether a given problem is very sensible to perturbations on the data or, on the contrary, is more “robust”. Problem geometry does have an impact on the sensitivity of...

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Bibliographic Details
Published in:Mathematical programming Vol. 147; no. 1-2; pp. 47 - 79
Main Author: Vera, Jorge R.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
Springer Nature B.V
Subjects:
Analysis
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computer science
Conics
Convex analysis
Estimates
Full Length Paper
Geometry
Impact analysis
Joints
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Perturbation methods
Robustness
Sensitivity analysis
Studies
Theoretical
Uncertainty
90C31
90C05
90C25
Geometric measures
Conic optimization
Sensitivity and stability in optimization
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:The effect of data perturbation and uncertainty has always been an important consideration in Optimization. It is important to know whether a given problem is very sensible to perturbations on the data or, on the contrary, is more “robust”. Problem geometry does have an impact on the sensitivity of the problem and in this paper we analyze this connection by developing bounds to the change in the optimal value of a conic linear problem in terms of some geometric measures related to the radius of inscribed and circumscribed balls to the feasible region of the problem. We also present a parametric analysis for Linear Programming which allows us to construct an estimate of safety limits for perturbations of the data. These results are developed in relation to questions in robust optimization.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0709-1