Factorable programming

2011 ◽  
Keyword(s):  
Factorable Programming

Tractable Relaxations of Composite Functions

2021 ◽  
Author(s):  
Taotao He ◽  
Mohit Tawarmalani
Keyword(s):  
Optimal Transport ◽  
Integral Formula ◽  
Transport Problem ◽  
Inner Function ◽  
Outer Function ◽  
Inner Functions ◽  
Separation Algorithm ◽  
Large Classes ◽  
Composite Functions ◽  
Factorable Programming

In this paper, we introduce new relaxations for the hypograph of composite functions assuming that the outer function is supermodular and concave extendable. Relying on a recently introduced relaxation framework, we devise a separation algorithm for the graph of the outer function over P, where P is a special polytope to capture the structure of each inner function using its finitely many bounded estimators. The separation algorithm takes [Formula: see text] time, where d is the number of inner functions and n is the number of estimators for each inner function. Consequently, we derive large classes of inequalities that tighten prevalent factorable programming relaxations. We also generalize a decomposition result and devise techniques to simultaneously separate hypographs of various supermodular, concave-extendable functions using facet-defining inequalities. Assuming that the outer function is convex in each argument, we characterize the limiting relaxation obtained with infinitely many estimators as the solution of an optimal transport problem. When the outer function is also supermodular, we obtain an explicit integral formula for this relaxation.

Global optimization of nonconvex factorable programming problems

2001 ◽  
Vol 89 (3) ◽  
pp. 459-478 ◽  
Author(s):  
Hanif D. Sherali ◽  
Hongjie Wang
Keyword(s):  
Global Optimization ◽  
Factorable Programming

Structure in Optimization: Factorable Programming and Functions

2012 ◽  
pp. 449-458
Author(s):  
Trond Steihaug ◽  
Shahadat Hossain ◽  
Laurent Hascoët
Keyword(s):  
Factorable Programming
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