Robust semidefinite programming problems with general nonlinear parameter dependence: Approaches using the DC-representations

Authors:
Yasuaki Oishi;Teodoro Alamo
Affiliations:
Department of Systems Design and Engineering, Nanzan University, Seireicho 27, Seto 489-0863, Japan;Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n.41092 Sevilla, Spain
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 13
Cited 0

Robust Convex Optimization

Mathematics of Operations Research
DC programming: overview

Journal of Optimization Theory and Applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications

Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Solutions to Uncertain Semidefinite Programs

SIAM Journal on Optimization
On Tractable Approximations of Uncertain Linear Matrix Inequalities Affected by Interval Uncertainty

SIAM Journal on Optimization
Solving convex programs by random walks

Journal of the ACM (JACM)
Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness

SIAM Journal on Matrix Analysis and Applications
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs

Mathematical Programming: Series A and B
Approximating the centroid is hard

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Brief paper: A set-membership state estimation algorithm based on DC programming

Automatica (Journal of IFAC)
Stability of networked control system with quantization

CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Brief paper: Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities

Automatica (Journal of IFAC)
Technical Communique: Robust sampled-data stabilization of linear systems: an input delay approach

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.14

Visualization

Abstract

Two conservative approaches are proposed to a semidefinite programming problem nonlinearly dependent on uncertain parameters. These approaches are applicable to general nonlinear parameter dependence not necessarily polynomial or rational. They are based on the mild assumption that the parameter dependence is expressed as the difference of two convex functions. The first approach uses constant bounds on the parameter dependence. Optimization of the bounds is reduced to convex nonsmooth minimization. The second approach uses parameter-dependent bounds for a less conservative result. Optimization of the bounds is immediate when the centroid is computable for the parameter set. Numerical examples are presented for illustration of the approaches.