RCADT - Mathematical Optimization Models. Duality Gap Problems скачать в хорошем качестве

RCADT - Mathematical Optimization Models. Duality Gap Problems

Duality Theory is a powerful and widely used tool in applied mathematics for several reasons: -The dual problem is always convex, even if the primal is not, The number of variables in the dual is equal to the number of constraints in - the primal, which is often less than the number of variables in the primal problem, and The maximum value reached by the dual problem is often equal to the minimum of the primal. In the mathematical theory of optimization, duality or duality principle is the principle that states that optimization problems can be seen from two perspectives: the primal problem or the dual problem. If the primal is a minimization problem, then the dual is a maximization problem (and vice versa). Any feasible solution to the primal problem (minimization) is at least as great as any feasible solution to the dual problem (maximization). Thus, the primal solution is an upper limit of the dual solution, and the dual solution is a lower limit of the primary solution. This fact is called weak duality. The duality gap is the difference between the primal solution and the dual solution. If d* is the optimal dual value and p* is the optimal primal value, then the duality gap is equal to p* - d*. For minimization issues, this value is always greater than or equal to 0. If the duality gap is zero, a strong duality is said to remain; otherwise, the gap is strictly positive and the weak duality remains    • RCADT - Mathematical Optimization Models. ...