- A Finitely Convergent Disjunctive Cutting Plane Algorithm for Bilinear Programming Hamed Rahimian (hrahimiclemson.edu) Sanjay Mehrotra (mehrotranorthwestern.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 [2018], 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. Download: [PDF]Entry Submitted: 01/31/2020Entry Accepted: 01/31/2020Entry Last Modified: 12/30/2020Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.