A hybrid approximation algorithm for convex multi-parametric quadratically constrained quadratic programs

Optimization and Engineering

Abstract

Abstract We present a solution method for convex multi-parametric quadratically constrained quadratic programs (mpQCQPs) with a single quadratic constraint. Past contributions have either approached these problems by treating the problem as a multi-parametric nonlinear program (mpNLP) and approximating the solution, or solving the mpQCQP exactly using symbolic computations. In this article, we develop a hybrid method that builds on these contributions and attempts to preserve nonlinearity in the solution where possible, while simultaneously avoiding the need for symbolic computations. We achieve this by computing the exact multi-parametric solution in all critical regions whose active set does not include the quadratic constraint. When the active set contains the quadratic constraint, we linearize the quadratic constraint and use the linearization to approximate the multi-parametric solution. By iteratively refining the linearization, our approach is able to approximate the solution up to a user-defined tolerance. Results indicate that our method is able to obtain high-quality solutions to instances whose exact solution is currently intractable.

Authors 4

1. Adrian W. Lipow Aachen Process Systems Engineering (AVT.SVT)

   RWTH Aachen University · Texas A&M University

   Affiliation as printed

   Process Systems Engineering (AVT.SVT), RWTH Aachen University, Aachen, Germany

   Texas A&M Energy Institute, Texas A&M University, College Station, USA

2. Dustin Kenefake

   University of Delaware · Texas A&M University

   Affiliation as printed

   Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, USA

   Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE, USA

   Texas A&M Energy Institute, Texas A&M University, College Station, USA

3. Elizabeth J. Abraham

   Texas A&M University

   Affiliation as printed

   Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, USA

   Texas A&M Energy Institute, Texas A&M University, College Station, USA

4. Efstratios N. Pistikopoulos corresponding

   Texas A&M University

   Affiliation as printed

   Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, USA

   Texas A&M Energy Institute, Texas A&M University, College Station, USA