One cutting plane algorithm using auxiliary functions

11th International Conference on "Mesh methods for boundary-value problems and applications"

Zabotin, I.Ya.^1 ; Kazaeva, K.E.^1

Kazan (Volga Region) Federal University, Kremlyovskaya st. 18, Kazan

420008, Russia^1

关键词: Algorithm for solving;    Auxiliary functions;    Convex programming problems;    Cutting plane algorithms;    Iteration points;    Linear programming problem;    Objective functions;    Penalty function;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012097/pdf
DOI  :  10.1088/1757-899X/158/1/012097

来源: IOP

【 摘 要 】

We propose an algorithm for solving a convex programming problem from the class of cutting methods. The algorithm is characterized by the construction of approximations using some auxiliary functions, instead of the objective function. Each auxiliary function bases on the exterior penalty function. In proposed algorithm the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. In connection with the above, the iteration points are found by solving linear programming problems. We discuss the implementation of the algorithm and prove its convergence.