- Complexity Analysis of a Trust Funnel Algorithm for Equality Constrained Optimization Frank E. Curtis (frank.e.curtisgmail.com) Daniel P. Robinson (daniel.p.robinsonjhu.edu) Mohammadreza Samadi (mos213lehigh.edu) Abstract: 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 $\epsilon$-feasible point and a second phase to seek optimality while maintaining at least $\epsilon$-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 $\epsilon$-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. Keywords: equality constrained optimization, nonlinear optimization, nonconvex optimization, trust funnel methods, worst-case iteration complexity Category 1: Nonlinear Optimization Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Lehigh ISE/COR@L Technical Report 16T-03, Bethlehem, PA, USA Download: [PDF]Entry Submitted: 01/02/2017Entry Accepted: 01/02/2017Entry Last Modified: 07/02/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.