A Mehrotra type predictor-corrector interior-point algorithm for linear programming
Soodabeh Asadi Hossein Mansouri
Numerical Algebra, Control & Optimization 2019, 9(2): 147-156 doi: 10.3934/naco.2019011

In this paper, we analyze a feasible predictor-corrector linear programming variant of Mehrotra's algorithm. The analysis is done in the negative infinity neighborhood of the central path. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The complexity result establishes an improvement of factor $ n^3 $ in the theoretical complexity of an earlier presented variant in [2], which is a huge improvement. We examine the performance of our algorithm by comparing its implementation results to solve some NETLIB problems with the algorithm presented in [2].

keywords: Interior-point algorithm linear programming central path predictor-corrector iteration complexity
A difference of convex optimization algorithm for piecewise linear regression
Adil Bagirov Sona Taheri Soodabeh Asadi
Journal of Industrial & Management Optimization 2019, 15(2): 909-932 doi: 10.3934/jimo.2018077

The problem of finding a continuous piecewise linear function approximating a regression function is considered. This problem is formulated as a nonconvex nonsmooth optimization problem where the objective function is represented as a difference of convex (DC) functions. Subdifferentials of DC components are computed and an algorithm is designed based on these subdifferentials to find piecewise linear functions. The algorithm is tested using some synthetic and real world data sets and compared with other regression algorithms.

keywords: Regression analysis nonsmooth optimization nonconvex optimization DC optimization subdifferential

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