A continuous time dynamical system approach for solving robust optimization

Keivan Ebrahimi, Nicola Elia, Umesh Vaidya

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We propose a dynamical system-based approach for solving robust optimization problems. The well-known continuous-time dynamical system for solving deterministic optimization problems arises in the form of primal-dual gradient dynamics where the vector field is derived as the gradient of the Lagrangian. The new continuous-time dynamical system we introduce for solving robust optimization problems differs from the primal-dual dynamics in the sense that the vector field is not derived as the gradient of the Lagrangian function. We call this new dynamical system as saddle point dynamics. In the saddle point dynamics, the uncertain variable arises as a dynamical state. For a general class of robust optimization problem, where the cost function is convex in decision variable and concave in uncertain variable, we show that the robust optimal solution can be recovered as a globally asymptotically stable equilibrium point of the saddle point dynamical system. Simulation results are presented to demonstrate the capability of this new dynamical system to solve various robust optimization problems. We also compare our proposed approach with existing methods based on robust counterpart and scenario-based random sampling.

Original languageEnglish (US)
Title of host publication2019 18th European Control Conference, ECC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1479-1485
Number of pages7
ISBN (Electronic)9783907144008
DOIs
StatePublished - Jun 2019
Event18th European Control Conference, ECC 2019 - Naples, Italy
Duration: Jun 25 2019Jun 28 2019

Publication series

Name2019 18th European Control Conference, ECC 2019

Conference

Conference18th European Control Conference, ECC 2019
CountryItaly
CityNaples
Period6/25/196/28/19

Bibliographical note

Funding Information:
Financial support from the National Science Foundation grants CNS-1329915, ECCS-1150405, CIF-1220643, ECCS-1810079 and also AFOSR AF FA-9550-15-1-0119 are gratefully acknowledged. K. Ebrahimi and U. Vaidya are with the Department of Electrical & Computer Engineering, Iowa State University, Ames, IA. N. Elia is with the Dept. of Electrical and Computer Engineering, University of Minnesota, Twin Cities. nelia@umn.edu, ugvaidya@iastate.edu,

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