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Newton methods for solving two classes of nonsmooth equations

Yan Gao (2001)

Applications of Mathematics

The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not...

Nonsmooth equations approach to a constrained minimax problem

Yan Gao, Xuewen Li (2005)

Applications of Mathematics

An equivalent model of nonsmooth equations for a constrained minimax problem is derived by using a KKT optimality condition. The Newton method is applied to solving this system of nonsmooth equations. To perform the Newton method, the computation of an element of the b -differential for the corresponding function is developed.

Non-uniqueness of almost unidirectional inviscid compressible flow

Pavel Šolín, Karel Segeth (2004)

Applications of Mathematics

Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with...

Currently displaying 261 – 280 of 502