# Difference between revisions of "Convex generalized disjunctive programming (GDP)"

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s.t.g(x) \leq 0\\ | s.t.g(x) \leq 0\\ | ||

− | + | r_{ki}(x) \leq M^{ki}(1-y_{ki})\quad k \in K,i \in D_k\\ | |

− | + | \sum_{i \in D_k} y_{ki} = 1\quad k \in K\\ | |

+ | Hy \geq h\\ | ||

+ | x^{lo} \leq x \leq x^{up}\\ | ||

+ | x \in \Re^n\\ | ||

− | + | y_{ki} \in {0,1} \quad k \in K, i \in D_k \end{align}</math> | |

+ | |||

+ | |||

+ | Notice that the boolean term from the original GDP has been converted into a numerical {0,1}. The logic relations have also been converted into linear integer constraints (Hy). | ||

+ | |||

+ | (<nowiki>https://kilthub.cmu.edu/articles/journal_contribution/Improved_Big-M_Reformulation_for_Generalized_Disjunctive_Programs/6467063</nowiki>) | ||

+ | |||

+ | This MINLP reformulation can now be used in well-known solvers (list them here) to calculate a solution. | ||

== Numerical Example == | == Numerical Example == |

## Revision as of 17:23, 21 November 2020

Edited By: Nicholas Schafhauser, Blerand Qeriqi, Ryan Cuppernull

## Introduction

## Theory

## Methodology

The two most common ways of reformulating a GDP problem into an MINLP are through Big-M (BM) and Hull Reformulation (HR). BM is the simpler of the two, while HR results in tighter relaxation (smaller feasible region) and faster solution times. (https://kilthub.cmu.edu/articles/A_hierarchy_of_relaxations_for_nonlinear_convex_generalized_disjunctive_programming/6466535)

Below is an example of the reformulation of the GDP problem from the Theory section reformulated into an MINLP by using the Big-M method.

Notice that the boolean term from the original GDP has been converted into a numerical {0,1}. The logic relations have also been converted into linear integer constraints (Hy).

(https://kilthub.cmu.edu/articles/journal_contribution/Improved_Big-M_Reformulation_for_Generalized_Disjunctive_Programs/6467063)

This MINLP reformulation can now be used in well-known solvers (list them here) to calculate a solution.