A Finitely Convergent Disjunctive Cutting Plane Algorithm for Bilinear Programming
Hamed Rahimian (hrahimiclemson.edu)
Abstract: In this paper we present and analyze a finitely-convergent disjunctive cutting plane algorithm to obtain an $\epsilon$-optimal solution or detect infeasibility of a general nonconvex continuous bilinear program. While the cutting planes are obtained in a manner similar to Saxena, Bonami, and Lee [Math. Prog. 130(2): 359-413, 2011] and Fampa and Lee , a feature of the algorithm that guarantees finite convergence is exploring near-optimal extreme point solutions to a current relaxation at each iteration. In this sense, the presented algorithm and its analysis extends the work of Owen and Mehrotra [Math. Prog. 89(3): 437-448, 2001] for solving mixed-integer linear programs to the general bilinear programs.
Keywords: Bilinear programming, Nonconvex programming, Disjunctive programming,Global optimization, Cutting planes
Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )
Category 2: Nonlinear Optimization (Quadratic Programming )
Category 3: Integer Programming (Cutting Plane Approaches )
Citation: Rahimian, H. and S. Mehrotra (2020). A finitely convergent disjunctive cutting plane algorithm for bilinear programming. Technical report, Northwestern University.
Entry Submitted: 01/31/2020
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