Worst case approach in convex minimization problems with uncertain data

2015/06/03 by Olli Mali, Mali, Olli
Decision Sciences · Engineering · Mathematics · #49N15 #49N30 #65N15 #Advanced Numerical Methods in Computational Mathematics #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1506.01236

openalex publication_date 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns quantitative analysis of errors generated by incompletely known data in convex minimization problems. The problems are discussed in the mixed setting and the duality gap is used as the fundamental error measure. The influence of the indeterminate data is measured using the worst case scenario approach. The worst case error is decomposed into two computable quantities, which allows the quantitative comparison between errors resulting from the inaccuracy of the approximation and the data uncertainty. The proposed approach is demonstrated on a paradigm of a nonlinear reaction-diffusion problem together with numerical examples.

Citations

• Conditioning of quasi-Newton methods for function minimization
• A family of variable-metric methods derived by variational means
• A new approach to variable metric algorithms

Related

• Nonconforming discretizations of convex minimization problems and\n precise relations to mixed methods
• Worst-case sensitivity
• Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis
• Correcting Convexity Bias in Function and Functional Estimate
• Bounding Optimality Gaps for Non-Convex Optimization Problems: Applications to Nonlinear Safety-Critical Systems