A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
dc.contributor.author | Dai, Y.H. | |
dc.contributor.author | Liu, X.W. | |
dc.contributor.author | Sun, Jie | |
dc.date.accessioned | 2023-04-16T10:08:15Z | |
dc.date.available | 2023-04-16T10:08:15Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Dai, Y.H. and Liu, X.W. and Sun, J. 2020. A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs. Journal of Industrial and Management Optimization. 16 (2): pp. 1009-1035. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/91435 | |
dc.identifier.doi | 10.3934/jimo.2018190 | |
dc.description.abstract |
With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is ecient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. | |
dc.language | English | |
dc.publisher | AMER INST MATHEMATICAL SCIENCES-AIMS | |
dc.subject | Science & Technology | |
dc.subject | Technology | |
dc.subject | Physical Sciences | |
dc.subject | Engineering, Multidisciplinary | |
dc.subject | Operations Research & Management Science | |
dc.subject | Mathematics, Interdisciplinary Applications | |
dc.subject | Engineering | |
dc.subject | Mathematics | |
dc.subject | Nonlinear programming | |
dc.subject | constrained optimization | |
dc.subject | infeasibility | |
dc.subject | interior-point method | |
dc.subject | global and local convergence | |
dc.subject | GLOBAL CONVERGENCE | |
dc.subject | ALGORITHM | |
dc.subject | OPTIMIZATION | |
dc.title | A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs | |
dc.type | Journal Article | |
dcterms.source.volume | 16 | |
dcterms.source.number | 2 | |
dcterms.source.startPage | 1009 | |
dcterms.source.endPage | 1035 | |
dcterms.source.issn | 1547-5816 | |
dcterms.source.title | Journal of Industrial and Management Optimization | |
dc.date.updated | 2023-04-16T10:08:14Z | |
curtin.department | School of Elec Eng, Comp and Math Sci (EECMS) | |
curtin.accessStatus | Open access | |
curtin.faculty | Faculty of Science and Engineering | |
curtin.contributor.orcid | Sun, Jie [0000-0001-5611-1672] | |
curtin.contributor.researcherid | Sun, Jie [B-7926-2016] [G-3522-2010] | |
dcterms.source.eissn | 1553-166X | |
curtin.contributor.scopusauthorid | Sun, Jie [16312754600] [57190212842] | |
curtin.repositoryagreement | V3 |