First and Second Order Optimality Conditions for the Control of\n Fokker-Planck Equations

2020/02/10 by M. Soledad Aronna, Aronna, M. Soledad, Fredi Tröltzsch +1 · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #35Q84 #49J20 #49K20 #49K27 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2002.03988

openalex publication_date 2020/02/10 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this article we study an optimal control problem subject to the\nFokker-Planck equation \
partial_t
rho -
nu
Delta
rho -
rm div \n
big(
rho B[u]
big) = 0. The control variable u is time-dependent and\npossibly multidimensional, and the function B depends on the space variable\nand the control. The cost functional is of tracking type and includes a\nquadratic regularization term on the control. For this problem, we prove\nexistence of optimal controls and first order necessary conditions. Main\nemphasis is placed on second order necessary and sufficient conditions.\n

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