We introduce a new class of inverse optimization problems in which an input solution is given together with k linear weight functions, and the goal to modify weights by same deviation vector p so that becomes optimal respect each them, while minimizing ‖p‖1. In particular, we concentrate on three multiple functions: shortest s−t path, bipartite perfect matching, arborescence problems. Using LP ...

and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫