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A hybrid method of nonlinear programming using curvilinear descent. (English. Russian original) Zbl 0604.90115
Sov. Math. 30, No. 2, 87-91 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 2(285), 61-64 (1986).
We consider the problem of finding \[ \min \{f_ 0(x)| x\in D\},\quad D=\{x\in R^ n| f_ i(x)\leq 0,\quad i\in I\}, \] where I is a finite set of indices, \(f_ i(x),\) \(i\in \bar I=I\cup \{0\}\) are fairly smooth functions, and D is a bounded set. We propose a two-phase solution method which develops a permissible sequence of points and combines global convergence for the relatively small calculational (far from optimal) \(\cos ts\) and a high rate of convergences in the neighborhood of the solution. In the first phase of the method descent occurs along possible directions. In the second phase, which is characteristic for iteration points that are fairly close to the solution, the descent goes along the second-order curves which do not derive from the permissible domain.
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods