2017/07/02 by Curtis, Frank E., Robinson, Daniel P., Samadi, Mohammadreza · 1 citation
#Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1707.00337
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an ε-feasible point and a second phase to seek optimality while maintaining at least ε-feasibility. A two-phase approach of this kind based on a cubic regularization methodology was recently proposed along with a supporting worst-case iteration complexity analysis. Unfortunately, however, in that approach, the objective function is completely ignored in the first phase when ε-feasibility is sought. The main contribution of the method proposed in this paper is that the same worst-case iteration complexity is achieved, but with a first phase that also accounts for improvements in the objective function. As such, the method typically requires fewer iterations in the second phase, as the results of numerical experiments demonstrate.