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[The unconstrained optimization problem is presented: the derivative and the derivative-free methods, as well as the optimality conditions are discussed. A short presentation of the two-level random search method for the unconstrained optimization of functions, for which the derivative information is not known, is given. Some open problems associated to this method are also shown. It is emphasized that for derivative-free methods like the one developed in this book, the only thing we can obtain is a point, where the minimizing function value is smaller or equal to the value in its initial point. Nothing can be said about its optimality, but having in view the scarcity of information on the minimizing function, mainly derivative, the result obtained may be of use for practical considerations.]
Published: Apr 1, 2021
Keywords: Unconstrained optimization; Derivative searching methods; Derivative-free searching methods; Optimality conditions
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