Such a problem may have multiple feasible regions and multiple locally optimal points within each region. Convex problems can be solved efficiently up to very large size.Ī non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below. Several methods - notably Interior Point methods - will either find the globally optimal solution, or prove that there is no feasible solution to the problem. With a convex objective and a convex feasible region, there can be only one optimal solution, which is globally optimal. In a convex optimization problem, the feasible region - the intersection of convex constraint functions - is a convex region, as pictured below. Conic optimization problems - the natural extension of linear programming problems - are also convex problems. Linear functions are convex, so linear programming problems are convex problems. Convex Optimization ProblemsĪ convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing. But Frontline System's Premium Solver Platform products includes an automated test for convexity of your problem functions. The issue has been that, unless your objective and constraints were linear, it was difficult to determine whether or not they were convex. Tyrrell Rockafellar, in SIAM Review, 1993Ĭonvex optimization problems are far more general than linear programming problems, but they share the desirable properties of LP problems: They can be solved quickly and reliably up to very large size - hundreds of thousands of variables and constraints. ".in fact, the great watershed in optimization isn't between linearity and nonlinearity, but convexity and nonconvexity."
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |