A combined homotopy interior point method for convex nonlinear programming
type: Item
instance of: scholarly article
title: A combined homotopy interior point method for convex nonlinear programming
zbMATH Open document ID: 0898.90100
DOI: 10.1016/S0096-3003(96)00086-0
author: Zhenghua Lin
author: Bo Yu
author: Guochen Feng
published in: Applied Mathematics and Computation
publication date: 1997-10-07T00:00:00Z
review text: The authors present a new interior point method -- combined homotopy interior point method (CHIP method) for convex nonlinear programming. Without strict convexity of the logarithmic barrier function and boundedness and nonemptiness of the solution set, it is proved that for any \(\varepsilon>0\), an \(\varepsilon\)-solution of the problem can be obtained by the CHIP method. In Section 2, the combined homotopy is given, existene of the combined homotopy path is proved, and limit properties of the combined homotopy path are discussed. In Section 3, results for linear programming are formulated, and it is demonstrated by a simple example that for those problems without strict convexity of the logarithmic barrier function and nonemptiness and boundedness of the solution set, the well-known center path-following method does not work while the CHIP method does. In Section 4, some numerical examples are given and some concluding remarks are made.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 1071578
zbMATH Keywords: CHIP method
zbMATH Keywords: combined homotopy interior point method
zbMATH Keywords: convex nonlinear programming
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1071578