scholarly journals Sharp Worst-Case Evaluation Complexity Bounds for Arbitrary-Order Nonconvex Optimization with Inexpensive Constraints

2020 ◽  
Vol 30 (1) ◽  
pp. 513-541
Author(s):  
Coralia Cartis ◽  
Nicholas I. M. Gould ◽  
Philippe L. Toint
Keyword(s):  
Nonconvex Optimization ◽  
Arbitrary Order ◽  
Worst Case ◽  
Complexity Bounds ◽  
Case Evaluation ◽  
Evaluation Complexity

Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

2016 ◽  
Vol 163 (1-2) ◽  
pp. 359-368 ◽  
Author(s):  
E. G. Birgin ◽  
J. L. Gardenghi ◽  
J. M. Martínez ◽  
S. A. Santos ◽  
Ph. L. Toint
Keyword(s):  
Nonlinear Optimization ◽  
High Order ◽  
Worst Case ◽  
Case Evaluation ◽  
Unconstrained Nonlinear Optimization ◽  
Evaluation Complexity

scholarly journals An interior point algorithm for solving linear optimization problems using a new trigonometric kernel function

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1471-1486
Author(s):  
S. Fathi-Hafshejani ◽  
Reza Peyghami
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Worst Case ◽  
Complexity Bounds ◽  
Linear Optimization Problems ◽  
Primal Dual ◽  
The Given

In this paper, a primal-dual interior point algorithm for solving linear optimization problems based on a new kernel function with a trigonometric barrier term which is not only used for determining the search directions but also for measuring the distance between the given iterate and the ?-center for the algorithm is proposed. Using some simple analysis tools and prove that our algorithm based on the new proposed trigonometric kernel function meets O (?n log n log n/?) and O (?n log n/?) as the worst case complexity bounds for large and small-update methods. Finally, some numerical results of performing our algorithm are presented.

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