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A primal-dual infeasible-interior-point algorithm for linear semi- infinite programming. (English) Zbl 0831.90113

Summary: We design an algorithm for solving linear semi-infinite programming problems by using the recently developed primal-dual infeasible-interior- point method for linear programming. The proposed algorithm enjoys the advantages of having “multiple inexactness” and “warm start” for computational efficiency. A convergence proof is included.

MSC:

90C34 Semi-infinite programming
90C05 Linear programming
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[1] Lin, C. J.; Fang, S.-C.; Wu, S. Y., A dual affine scaling based algorithm for solving linear semi-infinite programming problems, (Du, D. Z.; Sun, J., Advances in Optimization and Approximation (1994), Kluwer Academic Publishers), 217-234 · Zbl 0829.90128
[2] Fang, S.-C.; Wu, S. Y., An inexact approach to solving linear semi-infinite programming problems, Optimization, 28, 291-299 (1994) · Zbl 0819.90113
[3] Gustafson, S. A.; Kortanek, K. O., Numerical treatment of a class of semi-infinite programming problems, Naval Res. Logist., 20, 477-504 (1973) · Zbl 0272.90073
[4] Lai, H. C.; Wu, S. Y., On linear semi-infinite programming problems: An algorithm, Numerical Functional Analysis and Optimization, 13, 287-304 (1992) · Zbl 0758.90069
[5] Schafer, E., Ein Konstruktionsverfahten bei allgemeiner linearer Approximation, Numerical Mathematics, 18, 113-126 (1971) · Zbl 0257.65019
[6] Sheu, R.-L.; Wu, S. Y., A method of weighted centers for quadratic semi-infinite programming with warm start, (Technical Report (1994), Department of Mathematics, National Cheng-Kung University: Department of Mathematics, National Cheng-Kung University Tainan, Taiwan)
[7] Kojima, M.; Megiddo, N.; Mizuno, S., A primal-dual infeasible-interior-point algorithm for linear programming, Mathematical Programming, 61, 263-280 (1991) · Zbl 0808.90093
[8] Kojima, M.; Mizuno, S.; Yoshise, A., A primal-dual interior point method for linear programming, (Megiddo, N., Progress in Mathematical Programming: Interior-Point and Related Methods (1989), Springer-Verlag: Springer-Verlag New York), 29-47
[9] Anderson, E. J.; Nash, P., Linear Programming in Infinite-Dimensional Spaces: Theory and Applications (1987), John Wiley & Sons: John Wiley & Sons Chichester · Zbl 0632.90038
[10] Anderson, E. J.; Phipott, A. B., Infinite programming, (Lecture Notes in Econ. and Math. Systems, Vol. 259 (1985), Springer-Verlag: Springer-Verlag Berlin)
[11] Anderson, E. J.; Wu, S. Y., The continuous complementarity problem, Optimization, 22, 419-426 (1991) · Zbl 0734.90100
[12] Fang, S.-C.; Puthenpura, S., Linear Optimization and Extensions: Theory and Algorithms (1993), Prentice Hall: Prentice Hall Englewood Cliffs NJ
[13] (Fiacco, A. V.; Kortanek, K. O., Semi-infinite programming and applications. Semi-infinite programming and applications, Lecture Notes in Econ. and Math. Systems, Vol. 215 (1983), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0504.00017
[14] Gustafson, S. A., A three-phase algorithm for semi-infinite programs, (Fiacco, A. V.; Kortanek, K. O., Semi-Infinite Programming and Applications. Semi-Infinite Programming and Applications, Lecture Notes in Econ. and Math. Systems, Vol. 215 (1983), Springer-Verlag: Springer-Verlag Berlin), 138-157
[15] Gustafson, S. A.; Kortanek, K. O., Semi-infinite programming and applications, (Bachem, A.; Grotschel, M.; Korte, B., Mathematical Programming: The State and Art (1983), Springer-Verlag: Springer-Verlag Berlin), 132-157
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