LP and Approximation
... 1. If one problem has feasible solutions and a bounded objective function (and so has an optimal solution), then so does the other problem, so both the weak and the strong duality properties are applicable 2. If the optimal value of the primal is unbounded then the dual is infeasible. 3. If the opti ...
... 1. If one problem has feasible solutions and a bounded objective function (and so has an optimal solution), then so does the other problem, so both the weak and the strong duality properties are applicable 2. If the optimal value of the primal is unbounded then the dual is infeasible. 3. If the opti ...
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding ""best available"" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.