A class of counting problems asks for the number regions a central hyperplane arrangement. By duality, this is same as vertices zonotope. Efficient algorithms are known that solve problem by computing zonotope from its set generators. Here, we give an efficient algorithm, based on linear optimization oracle, performs inverse task and recovers generators vertices. We also provide variation algor...

applying robust optimization to solve product mix problem in automotive industries in this article, applying robust optimization in product mix problem in automotive industries is presented. the problem includes determining both the quantity and the identification of each product to produce to maximize profit. at first, the deterministic model will be presented. then, robust model of product mi...

We revisit the problem of online linear optimization in case where set feasible actions is accessible through an approximated oracle with a factor α multiplicative approximation guarantee. This setting particular interesting because it captures natural extensions well-studied offline problems that are NP-hard yet admit efficient algorithms. The goal here to minimize α-regret, which extension th...