Abstract
Primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) is an optimization method from a class of nonlinear rescaling techniques. Previous work does not discuss practical aspects of PDNRD method such as the explanation and the setting of the parameters. To complete this framework, the parameters were described. Moreover, PDNRD method was applied on two quadratic programming problems with quadratic constraints and recommendations about the setting of the parameters were made.
Highlights
The optimization theory is developing in parallel with the appearance of real-life problems and with the need to solve them
The situation in nonlinear programming (NLP) is more complicated in comparison with linear programming (LP) calculations and interior point methods are sometimes experiencing numerical difficulties
Another way how to improve the convergence of primaldual nonlinear rescaling (PDNR) method is a dynamic scaling parameter update [5] together with some globalization strategy
Summary
The optimization theory is developing in parallel with the appearance of real-life problems and with the need to solve them. The situation in NLP is more complicated in comparison with LP calculations and interior point methods are sometimes experiencing numerical difficulties This fact motivated Roman Polyak and Igor Griva to design an alternative method based on the nonlinear rescaling (NR) theory. PDNR method is locally convergent with the Qlinear convergence rate To improve these properties, PDNR method can be combined with another optimization method (e.g. the primal-dual path-following method) to obtain the global convergence [11]. PDNR method can be combined with another optimization method (e.g. the primal-dual path-following method) to obtain the global convergence [11] Another way how to improve the convergence of PDNR method is a dynamic scaling parameter update [5] together with some globalization strategy (e.g. a step length computation).
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