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Unconstrained multidimensional extremal problem contains the pattern search method for solving the multi-dimensional function extremum with Rosenbrock method for solving multidimensional function extremum simplex search method to solve the multi-dimensional function extremum Powell method for solving multidimensional function extremum with the steepest descent pole with Newton' s method for solving multidimensional function method for solving the multi-dimensional function extremum with conjugate gradient method to solve the multi-dimensional function extremum modified Newton method for solving multidimensional function extremum with DFP method to solve the multi-dimensional function extremum BFGS method for solving multidimensional seeking positive definite quadratic function extremum function extremum trust region method for solving multidimensional function extremum with explicit steepest descent method