Lack of Equality between Abel and Cesaro Limits in Discrete Optimal Control and the Implied Duality Gap

2020/10/27 by Ilya Shvartsman, Shvartsman, Ilya
Computer Science · Engineering · #40G10 #49N15 #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2010.14676

openalex publication_date 2020/10/27 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28

Abstract

In a recent paper it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper we construct an example of a problem satisfying the assumptions of the aforementioned paper, where Cesaro and Abel limits are different.

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