A central path interior point method for nonlinear programming and its local convergence. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Qiu, Songqiang; Chen, Zhongwen
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 12(2018)
• Page Start: 2471
• Page End: 2495
• Publication Date: 2018-12-02
• Subjects: Nonlinear programming -- primal–dual interior-point method -- trust-funnel-like method -- central path -- local convergence; 90C30 -- 90C51; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1400663
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial steps and a central path technique is used to keep the iterate bounded away from 0 and not to deviate too much from the central path. A trust-funnel-like strategy is adopted to drive convergence. We also use second-order correction (SOC) steps to achieve fast local convergence by avoiding Maratos effect. Furthermore, the presented algorithm can avoid the blocking effect. It also does not suffer the blocking of productive steps that other trust-funnel-like algorithm may suffer. We show that, under second-order sufficient conditions and strict complementarity, the full Newton step (combined with an SOC step) will be accepted by the algorithm near the solution, and hence the algorithm is superlinearly local convergent. Numerical experiments results, which are encouraging, are reported.