An Efficient Penalty Method without a Line Search for Nonlinear Optimization

In this work, we integrate some new approximate functions using the logarithmic penalty method to solve nonlinear optimization problems. Firstly, we determine the direction by Newton's method. Then, we establish an efficient algorithm to compute the displacement step according to the direction. Finally, we illustrate the superior performance of our new approximate function with respect to the line search one through a numerical experiment on numerous collections of test problems.