A penalty method for nonlinear programming

This paper presents a variant of logarithmic penalty methods for nonlinear convex programming. If the descent direction is obtained through a classical Newton-type method, the line search is done on a majorant function. Numerical tests show the efficiency of this approach versus classical line searches.

Method for finding majorant function estimates required to determine Picard’s successive approximations convergence domain

This paper deals with convergence of Picard’s successive approximations, which give a solution for perturbed body motion differential equations system through constructing a majorizing linear differential equation. The task is to determine the domain of used variables where these successive approximations converge and to estimate how large the error will be if we take a finite number of approximations. A method for finding majorant function estimates required to determine Picard’s successive approximations convergence domain is constructed.

On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

We develop the Newton-Kantorovich method to solve the system of2×2nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.