A combined homotopy interior point method for convex nonlinear programming
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.
scientific article; zbMATH DE number 1071578
scientific article