Error Analysis for Convex Separable Programs: The Piecewise Linear Approximation and The Bounds on The Optimal Objective Value

摘要: The bounds have been established on the possible deviation of optimal objective value a separable, convex program from which is its piecewise linear approximation based given subdivision interval. By meant separable with proper convexity-concavity properties imply that any local optimum also global optimum. It further shown these are actually attainable, and therefore, cannot be improved in general. Some examples provided.Naturally, inquiry requires some study itself. function error determined assumptions—the boundedness first, or second, both derivatives—about original function. results derived for function, to determine nature minimum satisfying certain conditions; would applicable those ...