A central path interior point method for nonlinear programming and its local convergence

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.

Keywords:

• Nonlinear programming
• primal–dual interior-point method
• trust-funnel-like method
• central path
• local convergence

2010 AMS Subject Classifications:

• 90C30
• 90C51

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The Fundamental Research Funds for the Central Universities [2014QNA62].