On solving a class of linear semi-infinite programming by SDP method. (English) Zbl 1311.90160
Summary: In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on \([l,u]\) could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.
Keywords:
semi-infinite programming; nonnegative polynomial; SOS method; semi-definite programming; error boundReferences:
| [1] | DOI: 10.1137/1035089 · Zbl 0784.90090 · doi:10.1137/1035089 |
| [2] | DOI: 10.1007/s10898-009-9462-7 · Zbl 1220.90144 · doi:10.1007/s10898-009-9462-7 |
| [3] | DOI: 10.1007/s10107-003-0492-5 · Zbl 1073.90053 · doi:10.1007/s10107-003-0492-5 |
| [4] | Liping Zhang, SIAM J. Optim. 20 pp 2959– (2010) · Zbl 1229.90247 · doi:10.1137/090767133 |
| [5] | DOI: 10.1137/S0363012901398393 · Zbl 1046.90093 · doi:10.1137/S0363012901398393 |
| [6] | Reznick B, Contemp. Math. Am. Math. Soc. 253 pp 251– (2000) · doi:10.1090/conm/253/03936 |
| [7] | Prestel A, Positive polynomials: from Hilberts 17th problem to real algebra (2001) · Zbl 0987.13016 · doi:10.1007/978-3-662-04648-7 |
| [8] | Putinar M, Indiana Univ. Math. J. 42 pp 969– (1993) · Zbl 0796.12002 · doi:10.1512/iumj.1993.42.42045 |
| [9] | DOI: 10.1007/BF01443605 · JFM 20.0198.02 · doi:10.1007/BF01443605 |
| [10] | Powers V, Trans. Am. math. Soc. 352 pp 4677– (2000) · Zbl 0957.26004 · doi:10.1090/S0002-9947-00-02595-2 |
| [11] | Sun W, Optimization theory and methods: nonlinear programming (2006) · Zbl 1129.90002 |
| [12] | DOI: 10.1017/S0962492901000071 · Zbl 1105.65334 · doi:10.1017/S0962492901000071 |
| [13] | DOI: 10.1007/978-1-4612-1394-9 · doi:10.1007/978-1-4612-1394-9 |
| [14] | DOI: 10.1007/s10107-002-0347-5 · Zbl 1030.90082 · doi:10.1007/s10107-002-0347-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
