کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
476888 | 1446083 | 2012 | 10 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A hierarchy of relaxations for nonlinear convex generalized disjunctive programming A hierarchy of relaxations for nonlinear convex generalized disjunctive programming](/preview/png/476888.png)
We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of the relaxations increases as the number of conjuncts decreases, leading to a hierarchy of relaxations. We prove that the tightest of these relaxations, allows in theory the solution of the disjunctive convex program as a nonlinear programming problem. We present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed-integer program. Finally, we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs (GDP). This methodology is validated through a set of numerical examples.
Journal: European Journal of Operational Research - Volume 218, Issue 1, 1 April 2012, Pages 38–47