Abstract
The alpha-reformulation (alpha R) technique can be used to transform any nonconvex twice-differentiable mixed-integer nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is implemented in the a global optimization (alpha GO) algorithm solving the specified problem type to global optimality as a sequence of reformulated subproblems where the piecewise linear functions are refined in each step. The tightness of the underestimator has a large impact on the efficiency of the solution process, and in this paper it is shown how it is possible to reduce the approximation error by utilizing a piecewise quadratic spline function defined on smaller subintervals. The improved underestimator is also applied to test problems illustrating its performance.
Original language | Undefined/Unknown |
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Title of host publication | 11th International Conference on Chemical and Process Engineering - selected papers of ICheaP11 |
Editors | Sauro Pierucci, Jiří J. Klemeš |
Publisher | Associazione Italiana di Ingegneria Chimica |
Pages | 1321–1326 |
Number of pages | 6 |
ISBN (Print) | 978-88-95608-23-5 |
DOIs | |
Publication status | Published - 2013 |
MoE publication type | A4 Article in a conference publication |
Event | International Conference on Chemical and Process Engineering (ICheaP) - 11th International Conference on Chemical and Process Engineering (ICheaP) Duration: 2 Jun 2013 → 5 Jun 2013 |
Conference
Conference | International Conference on Chemical and Process Engineering (ICheaP) |
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Period | 02/06/13 → 05/06/13 |