Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling

Thai Doan Chuong (), Xinghuo Yu (), Andrew Eberhard (), Chaojie Li () and Chen Liu ()
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Thai Doan Chuong: Brunel University London
Xinghuo Yu: RMIT University
Andrew Eberhard: RMIT University
Chaojie Li: UNSW Sydney
Chen Liu: RMIT University

Journal of Global Optimization, 2024, vol. 90, issue 3, No 10, 811 pages

Abstract: Abstract In this paper, we consider a polynomial problem with equilibrium constraints in which the constraint functions and the equilibrium constraints involve data uncertainties. Employing a robust optimization approach, we examine the uncertain equilibrium constrained polynomial optimization problem by establishing lower bound approximations and asymptotic convergences of bounded degree diagonally dominant sum-of-squares (DSOS), scaled diagonally dominant sum-of-squares (SDSOS) and sum-of-squares (SOS) polynomial relaxations for the robust equilibrium constrained polynomial optimization problem. We also provide numerical examples to illustrate how the optimal value of a robust equilibrium constrained problem can be calculated by solving associated relaxation problems. Furthermore, an application to electric vehicle charging scheduling problems under uncertain discharging supplies shows that for the lower relaxation degrees, the DSOS, SDSOS and SOS relaxations obtain reasonable charging costs and for the higher relaxation degrees, the SDSOS relaxation scheme has the best performance, making it desirable for practical applications.

Keywords: Global optimization; Robust optimization; Equilibrium constraint; Semidefinite programming; Electric vehicle charging (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01421-0

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