Interior-point methods for convex programming

1992 ◽  
Vol 26 (3) ◽  
pp. 287-311 ◽  
Author(s):  
Florian Jarre
Keyword(s):  
Convex Programming ◽  
Interior Point ◽  
Interior Point Methods

scholarly journals On some efficient interior point methods for nonlinear convex programming

1991 ◽  
Vol 152 ◽  
pp. 169-189 ◽  
Author(s):  
K.O. Kortanek ◽  
Florian Potra ◽  
Yinyu Ye
Keyword(s):  
Convex Programming ◽  
Interior Point ◽  
Interior Point Methods

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

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