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Zbl 1149.90160
Liu, Guo-xin
A homotopy interior point method for semi-infinite programming problems. (English)
[J] J. Glob. Optim. 37, No. 4, 631-646 (2007). ISSN 0925-5001; ISSN 1573-2916/e

The article presents a homotopy method for the solution of standard semi-infinite programs (SIPs) with convex lower level problems. The main idea is to look at the combined stationarity conditions of the upper and lower level problems and solve the resulting degenerate equation by a homotopy approach. The homotopy path is shown to be a smooth curve which ends at a point that satisfies the combined stationarity conditions. This curve consists of interior points of its natural embedding set, but it should be pointed out that the corresponding decision variables are not necessarily interior points of the feasible set of SIP, as the title of the paper might suggest. Tracing the homotopy path numerically from a given starting point gives rise to a globally convergent algorithm for SIP. Some preliminary numerical results illustrate the presented approach.
[Oliver Stein (Aachen)]

MSC 2000:: *90C34 Semi-infinite programming
90C46 Optimality conditions, duality

Keywords: Karush-Kuhn-Tucker system; path following; global convergence

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