2020/07/03 by Luis M. Briceño-Arias, Julio Deride, Briceño-Arias, Luis +5 · 1 citation
Business, Management and Accounting · Computer Science · Decision Sciences · Social Sciences · #47H05 #65K05 #65K15 #90C25 #90C90 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization #Sustainable Supply Chain Management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2007.01983
openalex publication_date 2020/07/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this work we study a constrained monotone inclusion involving the normal\ncone to a closed vector subspace and a priori information on primal solutions.\nWe model this information by imposing that solutions belongs to the fixed point\nset of an averaged nonexpansive mapping. We characterize the solutions using an\nauxiliary inclusion that involves the partial inverse operator. Then, we\npropose the primal-dual partial inverse splitting and we prove its weak\nconvergence to a solution of the inclusion, generalizing several methods in the\nliterature. The efficiency of the proposed method is illustrated in two\nnon-smooth convex optimization problems whose constraints have vector subspace\nstructure. Finally, the proposed algorithm is applied to find a solution to a\nstochastic arc capacity expansion problem in transport networks.\n