A Class Of Non-monotone Trust Region Methods For Equality Constrained Optimization Problem

Grippo (1986) first presented Newton and truncated Newton method with the nonmonotone line search technique for unconstrained optimization. Since the idea of non-monotone method abandons the restriction of the descent property of the value of the object function, which allows the sequence of iterates to follow the bottom of curved narrow valleys (a common occurrence in difficult nonlinear problems) much more loosely, which hopefully results in longer and more efficient steps, and Marotos effect can be overcome in a way, many authors regard it. This paper mainly discusses a nonomontone trust region algorithm for equality constrained optimization with nondifferentiable merit function. Under certain conditions, the global convergence of the algorithm are proved. And numerical experiments show that the nonmonotone algorithms are generally better than monotone algorithms, especially for difficult nonlinear problems.