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Sequence of polyhedral relaxations for nonlinear univariate functions

Sundar, Kaarthik / Sanjeevi, Sujeevraja / Nagarajan, Harsha

Given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

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Sequence of polyhedral relaxations for nonlinear univariate functions

Sundar, Kaarthik / Sanjeevi, Sujeevraja / Nagarajan, Harsha

Given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

Sequence of polyhedral relaxations for nonlinear univariate functions

Sundar, Kaarthik / Sanjeevi, Sujeevraja / Nagarajan, Harsha

Given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

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Title:

Sequence of polyhedral relaxations for nonlinear univariate functions

Additional title:

Optim Eng

Contributors:

Sundar, Kaarthik (author) / Sanjeevi, Sujeevraja (author) / Nagarajan, Harsha (author)

Published in:

Optimization and Engineering ; 23 ; 877-894

Publication date:

2022-06-01

Size:

18 pages

ISSN:

1573-2924 , 1389-4420

DOI:

https://doi.org/10.1007/s11081-021-09609-z

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

Piecewise relaxation , Univariate function , Global optimization , convex hull , Continuous relaxation Mathematics , Optimization , Engineering, general , Systems Theory, Control , Environmental Management , Operations Research/Decision Theory , Financial Engineering , Mathematics and Statistics

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