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A smoothing projected Newton-type method for semismooth equations with bound constraints. (English) Zbl 1177.90389
Summary: This paper develops a smoothing algorithm to solve a system of constrained equations. Compared with the traditional methods, the new method does not need the continuous differentiability assumption for the corresponding merit function. By using some perturbing technique and suitable strategy of the chosen search direction, we find that the new method not only keeps the strict positivity of the smoothing variable at any non-stationary point of the corresponding optimization problem, but also enjoys global convergence and locally superlinear convergence. The former character is the key requirement for smoothing methods. Some numerical examples arising from semi-infinite programming (SIP) show that the new algorithm is promising.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C30 Nonlinear programming
65H10 Numerical computation of solutions to systems of equations
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