The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Jointly Constrained Biconvex Programming
Abstract
This paper presents a branch-and-bound algorithm for minimizing the sum of a convex function in x, a convex function in y and a bilinear term in x and y over a closed set. Such an objective function is called biconvex with biconcave functions similarly defined. The feasible region of this model permits joint constraints in x and y to be expressed. The bilinear programming problem becomes a special case of the problem addressed in this paper. We prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point. The algorithm is proven to converge to a global solution of the nonconvex program. We discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs, for which the algorithm has been implemented.
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Cites
An algorithm for quadratic programming
Frank, M., & Wolfe, P. (1956) · Naval Research Logistics Quarterly · doi:10.1002/nav.3800030109 · Cited by 3,030
Introduction to matrix computations
Stewart, G. W. (1973) · International Linear Collider · Cited by 2,381
Noble, B. (1969) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 1,349
Equilibrium Points of Bimatrix Games
Lemke, C. E., & Howson, Jr. (1964) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0112033 · Cited by 1,231
An Algorithm for Separable Nonconvex Programming Problems
Falk, J. E., & Soland, R. M. (1969) · Management Science · doi:10.1287/mnsc.15.9.550 · Cited by 409
Self-citationTwo-person nonzero-sum games and quadratic programming
Mangasarian, O. L., & Stone, H. (1964) · Journal of Mathematical Analysis and Applications · doi:10.1016/0022-247x(64)90021-6 · Cited by 152
Cited by
Adjiman, C. S., Dallwig, S., Floudas, C. A., & Neumaier, A. (1998) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(98)00027-1 · Cited by 526
?BB: A global optimization method for general constrained nonconvex problems
Androulakis, I. P., Maranas, C. D., & Floudas, C. A. (1995) · Journal of Global Optimization · doi:10.1007/bf01099647 · Cited by 465
Mixed Integer Linear Programming Formulation Techniques
Vielma, J. P. (2015) · SIAM Review · doi:10.1137/130915303 · Cited by 358
Global optimization for the parameter estimation of differential-algebraic systems
Esposito, W. R., & Floudas, C. A. (2000) · Industrial & Engineering Chemistry Research · doi:10.1021/ie990486w · Cited by 188
On the Computational Complexity of Stochastic Controller Optimization in POMDPs
Vlassis, N., Littman, M. L., & Barber, D. (2012) · ACM Transactions on Computation Theory · doi:10.1145/2382559.2382563 · Cited by 65
Metadata
- Authors
- Al-Khayyal, F. A., & Falk, J. E.
- Venue
- Mathematics of Operations Research
- Published
- 1983-05
- Volume
- 8
- Issue
- 2
- Pages
- 273-286
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2048881327
- Cited by
- 553
- References
- 6
- FWCI
- 2.50
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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