Abstract
This paper suggests a new regularized penalty method for poly-linear functions. Until our knowledge it is the first time that a regularization approach solution for poly-linear programming is reported in the literature. We propose a penalty function depending on two parameters μ and δ for ensuring the strong convexity and the existence of a unique solution involving equality and inequality constraints. We prove that if the penalty parameter μ tends to zero then the solution of the original problem converges to a unique solution with the minimal weighted norm. We introduce a recurrent procedure based on the projection-gradient method for finding the extremal points and we also prove the convergence of the method. We develop an example for game theory and additional example for portfolio optimization employing the proposed regularization method for Markov chains involving the definition of a poly-linear function.
Original language | English |
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Pages (from-to) | 267-286 |
Number of pages | 20 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 328 |
DOIs | |
State | Published - 15 Jan 2018 |
Keywords
- Ill-posed problem
- Markov chains
- Poly-linear programming
- Regularization
- Tikhonov