Special ordered sets and an application to gas supply operations planning

1988 ◽  
Vol 42 (1-3) ◽  
pp. 69-84 ◽  
Author(s):  
J. A. Tomlin
Keyword(s):  
Ordered Sets ◽  
Operations Planning ◽  
Special Ordered Sets ◽  
Gas Supply

scholarly journals A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

2019 ◽  
Vol 44 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Joey Huchette ◽  
Juan Pablo Vielma
Keyword(s):  
Piecewise Linear ◽  
Expressive Power ◽  
Complete Characterization ◽  
Linear Functions ◽  
Mixed Integer ◽  
Ordered Sets ◽  
Special Ordered Sets ◽  
Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

Global optimization using special ordered sets

1976 ◽  
Vol 10 (1) ◽  
pp. 52-69 ◽  
Author(s):  
E. M. L. Beale ◽  
J. J. H. Forrest
Keyword(s):  
Global Optimization ◽  
Ordered Sets ◽  
Special Ordered Sets

scholarly journals A note of the knapsack problem with special ordered sets

1981 ◽  
Vol 1 (1) ◽  
pp. 18-22 ◽  
Author(s):  
Ellis L. Johnson ◽  
Manfred W. Padberg
Keyword(s):  
Knapsack Problem ◽  
Ordered Sets ◽  
Special Ordered Sets
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