Al-Khayyal, F. and J. Falk: 1983, `Jointly constrained biconvex programming'. Mathematics of Operations Research 8, 273--286. Home/Search Document Not in Database Summary Related Articles Check |
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Lower Bound Functions for Polynomials - Garloff, Jansson, Smith (2003) (1 citation) (Correct)
.... case of linear integer problems, and later also for special structured continuous global optimisation problems; see for example the monographs of Floudas [9] Horst and Pardalos [13] and Parker and Rardin [22] Linear relaxations for bilinear problems were rst considered by Al Khayyal and Falk [2]. They use the convex envelope of bilinear terms in order to obtain a relaxation. For developments and improvements for special structured continuous global optimisation problems that include non convexities introduced by concave univariate, bilinear and linear fractional terms the reader is ....
....optimality has to be veri ed. Veri cation algorithms for linear programming problems are described in [16] and [18] for example. 6 Convex envelopes Convex envelopes are of primary importance in many applications since they represent the uniformly best convex underestimating function, e.g. [2, 14]. Now the question arises under which conditions the lower bound functions introduced in Section 3 provide the lower convex envelope of a polynomial p. Of special interest is the case in which is concave. Figure 6.1 The lower bound function coincides with the lower convex envelope. ....
F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Math. Oper. Res., 8:273{ 286, 1983.
Lower Bound Functions for Polynomials - Garloff, Jansson (1 citation) (Correct)
....has to be verified. Verification algorithms for linear programming problems are described in [15] and [17] for example. 11 6 Convex envelopes Convex envelopes are of primary importance in many applications since they represent the uniformly best convex underestimating function, e.g. [2, 13]. Now the question arises under which conditions the lower bound functions introduced in Section 3 provide the lower convex envelope of a polynomial p. Of special interest is the case in which p is concave. Figure 6.1 The lower bound function coincides with the lower convex envelope. ....
F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Math. Oper. Res., 8:273--286, 1983.
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Al-Khayyal, F. and J. Falk: 1983, `Jointly constrained biconvex programming'. Mathematics of Operations Research 8, 273--286.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2):273-286, 1983.
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F. Al-Khayyal and J. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8:273--286, 1983.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2):273-286, 1983.
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Al-Khayyal, F. and J. Falk: 1983, `Jointly Constrained Biconvex Programming'. Mathematics of Operations Research pp. Vol.8, No.2, 273--286.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, pages 8:2:273--286, 1983.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, pages 8:2:273--286, 1983.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, pages Vol.8, No.2, 273286, 1983.
Global Filtering Algorithms Based on Linear Relaxations - Lebbah, Michel, RUEHER (2003) (1 citation) (Correct)
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, pages 8:2:273286, 1983.
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F.A. Al-Khayyal and J.E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, pages 8:2:273286, 1983.
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Faiz A. Al-Khayyal and J.E. Falk. Jointly Constrained Biconvex Programming. Annals of Operations Research, 25:169--180, 1983.
Global Optimization of Mixed-Integer Nonlinear Programs.. - Tawarmalani, Sahinidis (2003) (3 citations) (Correct)
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F. A. Al-Khayyal and J. E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8:273--286, 1983.
Global Optimization of Nonconvex Nonlinear Programs Using.. - Epperly (1995) (4 citations) (Correct)
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F. A. Al-Khayyal and J. E. Falk. Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2):273--286, May 1983.
New Properties and Computational Improvement - Of The Gop (Correct)
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Al-Khayyal, F.A., and Falk, J.E., Jointly Constrained Biconvex Programming, Mathematics of Operations Research, 8, (1983).
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