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Nature inspired and classic metaheuristic algorithms for global unconstrained optimization problems: A comparative analysis

Marinaki Magdalini, Marinakis Ioannis

Πλήρης Εγγραφή

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Περίληψη

The chapter deals with the parametric linear-convex mathematical programming (MP) problem in a Hilbert space. Based on the ideology of the perturbation method, we study an MP problem depending on an infinite-dimensional parameter which is additively contained in the equality and inequality constraints. We consider an algorithm of dual regularization for this parametric MP problem that is stable with respect to input data errors. In the algorithm, the duality of the orig- inal optimization problem is solved directly on the basis of Tikhonov regularization. Simultaneously, our purpose is to study the properties of its convergence depending on differential properties of the value function (S-function) of the parametric MP prob- lem. We consider also an iterative regularization of the dual regularization algorithm and stopping rule for the iteration process in the case of a finite fixed error in the input data. An important point in the dual regularization algorithm is that the process of dual regularization, together with the constructive generation of a minimizing sequence, leads in a natural way to necessary optimality conditions in the original MP prob- lem. Thus, the classical construction of the Lagrangian, together with the Tikhonov regularization of the dual problem, provides not only an algorithm for the numerical solution of the original optimization problembut also a new approach to the derivation of necessary optimality conditions.

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