Sequence of polyhedral relaxations for nonlinear univariate functions

Sundar, Kaarthik; Sanjeevi, Sujeevraja; Nagarajan, Harsha

doi:10.1007/s11081-021-09609-z

Sequence of polyhedral relaxations for nonlinear univariate functions

Journal Article · Sat Apr 17 00:00:00 EDT 2021 · Optimization and Engineering

DOI:https://doi.org/10.1007/s11081-021-09609-z· OSTI ID:1874908

^[1]; Sanjeevi, Sujeevraja ^[2]; ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sabre, Southlake, TX (United States)

Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1874908

Report Number(s):: LA-UR-20-23980

Journal Information:: Optimization and Engineering, Journal Name: Optimization and Engineering Journal Issue: 2 Vol. 23; ISSN 1389-4420

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Sequence of polyhedral relaxations for nonlinear univariate functions

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