Complexity of general continuous minimization problems: a survey

The problem of finding a local or a global minimum of a real function on a set S⊆ ℝ n occurs in many real world problems. When f is a general nonlinear function, deterministic as well as stochastic algorithms have been proposed. The numerical cost of these algorithms, that can be the number of function evaluations or the number of elementary operations required when executed, has been investigated in the last few years. In this paper, we survey the main results by classifying them according to the field they refer to: local minimization, global minimization and checking the optimality conditions. Further, some results concerning the information that an algorithm may use, are surveyed.

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