Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints

Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints

In this paper, we developed a novel algorithmic approach for the solution of multi-parametricnon-convex programming problems with continuous decision variables. The basic idea of the proposedapproach is based on successive convex relaxation of each non-convex terms and sensitivity analysis theory. The proposed algorithm is implemented using MATLAB software package and numericalexamples are presented to illustrate the effectiveness and applicability of the proposed method onmulti-parametric non-convex programming problems with polyhedral constraints

___

  • [1] Li Z. and Ierapetritou G. M., A New Methodology for the General Multiparametric Mixed-Integer Linear Programming (MILP) Problems, Industrial & Engineering Chemistry Research, 46, 5141-5151 (2007).
  • [2] Dua V. Bozinis A. N. and Pistikopoulos N. E., A multi-parametric Programming Approach for mixedinteger quadratic engineering problems, Computers & Chemical Engineering, 26, 715-733 (2002).
  • [3] Pistikopous, N. E., Georgiads C. M. and Dua V., (Editors) Multiparametric programming: Theory, algorithm, and application, WILEY-VCH Verlag GmbH and Co. KGaA, (2007).
  • [4] Dua V., Pistikopoulos, E. N., An algorithm for the solution of multiparametric mixed integer linear programming problems, Annals of Operations Research, 99, 123 - 139 (2001).
  • [5] Fa´ısca P. N, Dua V., Rustem B., Saraiva M. P., Pistikopoulos N. E., Parametric global optimisation for bilevel programming, Journal of Global Optimization, 38, 609-623 (2006).
  • [6] Fa´ısca P. N., Saraiva M. P., Rustem B., Pistikopoulos N. E. A multiparametric programming approach for multilevel hierarchical and decentralized optimization problems, Computational Management Science, 6, 377-397 (2009).
  • [7] Tøndel P., Johansen T. A. and Bemporad A., Further Results on Multiparametric Quadratic Programming, in Proceedings of 42nd IEEE Conference on Decision and Control, 3, 3173-3178 (2003).
  • [8] Al-Khayyal A. F., Jointly constrained bilinear programms and related problems: An overview, Computers Math. applic, 19, 53-62 (1990).
  • [9] Adjiman S. C., Dallwing S., Floudas A. C., Neumaier A., A global optimization method, αBB, for general twice-differentiable constrained NLPs I.Theoretical advances, Computers and Chemical Engineering, 22, 1137 - 1158 (1998).
  • [10] Androulakis P. I., Maranas D. C., and Floudas A. C., αBB: A Global Optimization Method for General Constrained Nonconvex Problems, Journal of Global Optimization, 7, 337-363 (1995).
  • [11] Fiacco V. A., Sensitivity analysis for nonlinear programming using penalty methods, Mathematical Programming, 10, 287-311 (1976).
  • [12] Fiacco V. A., Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Acadamic press, (1983).