Convexity of Second-Order Cone Program in the Right Hand Side Parameter
Shourya Bose
TL;DR
This paper proves that the optimal value of a second-order cone program (SOCP) varies convexly with changes in the right hand side parameter, providing insights into the stability and sensitivity of SOCP solutions.
Contribution
The paper establishes the convexity of the SOCP optimal value with respect to the RHS parameter, a property not previously proven.
Findings
Optimal value of SOCP is convex in RHS parameter
Convexity property aids in sensitivity analysis
Enhances understanding of SOCP stability
Abstract
In this note we prove that the optimum value of a second-order cone program (SOCP) is convex in the right hand side (RHS) parameter.
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Taxonomy
TopicsOptimization and Variational Analysis · Risk and Portfolio Optimization · Optimization and Mathematical Programming