2009/06/18 by Julien Salomon, Salomon, Julien, Gabriel Turinici +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.0906.3361
openalex publication_date 2009/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation that can be applied to more nonlinear settings compatible with the hypothesis detailed below. In this framework, we show that the well-posedness of the general algorithm is related to a nonlinear evolution equation. We prove the existence of the solution to this equation and give important properties of the optimal control functional. Finally we show how the algorithm works for selected models from the literature and compare it with the gradient algorithm.