Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2007-012 (June 08, 2007)
An explicit exchange algorithm for linear semi-infinite programming
by Shunsuke Hayashi and Soon-Yi Wu
In this paper, we propose an explicit exchange algorithm for solving semiinfinite
programming problem (SIP) with second-order cone (SOC) constraints. We prove,
by using the slackness complementarity conditions, that the algorithm terminates in a finite
number of iterations and the obtained solution sufficiently approximates the original
SIP solution. In existing studies on SIPs, only the nonnegative constraints were considered,
and hence, the slackness complementarity conditions were separable to each component.
However, in our study, the existing componentwise analyses are not applicable anymore
since the slackness complementarity conditions are associated with SOCs. In order to
overcome such a difficulty, we introduce a certain coordinate system based on the spectral
factorization. In the numerical experiments, we solve some test problems to see the
effectiveness of the proposed algorithm.