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Using Regularization and Second Order Information in Outer Approximation for Convex MINLP

Jan Kronqvist (jakronqv***at***abo.fi)
David E. Bernal (bernalde***at***cmu.edu)
Ignacio E. Grossmann (grossmann***at***cmu.edu)

Abstract: In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is inspired by the level method and uses a regularization technique to reduce the step size when choosing new integer combinations. The second method combines ideas from both the level method and the sequential quadratic programming technique and uses a second order approximation of the Lagrangean when choosing the new integer combinations. The main idea behind the methods is to choose the integer combination more carefully in each iteration, in order to obtain the optimal solution in fewer iterations compared to the original outer approximation method. We prove rigorously that both methods will find and verify the optimal solution in a finite number of iterations. Furthermore, we present a numerical comparison of the methods based on 109 test problems, which illustrates the benefits of the proposed methods.

Keywords: Convex MINLP, Outer approximation, Level based method

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Preprint, January 2018

Download: [PDF]

Entry Submitted: 01/03/2018
Entry Accepted: 01/03/2018
Entry Last Modified: 01/08/2018

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