A multiparametric programming approach for mixed-integer quadratic engineering problems

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…Linear objective and constraints: extension of simplex algorithm -basis exchange. Bemporad et al [32]; Dua et al [98] Solve Linear Program (LP) and use sensitivity analysis to derive expressions. Use inactive inequalities and Lagrangian multipliers to define regions.…”

“…Employ a spatial branch-and-bound to obtain solution. Dua et al [98] Quadratic objective and linear constraints (mp-QP). Uses sensitivity analysis from Fiacco and Kyparisis [111] to obtain the exact expressions under convexity assumptions.…”

“…The parameter dependence of the objective function can be avoided using the , 96, 201, 257, 294, 359] 2-norm Hybrid system [7,14,98,152,257] *:…”

Global optimization in the 21st century: Advances and challenges

“…Wang and Achenie (2002a) studied the molecular design of solvents for extractive fermentation including solvent attributes such as biocompatibility, inertness and phase splitting, introduced a group contribution framework which results in a conconvex MINLP model, studied a local MINLP algorithm, OA/ER/AP, and applied it to case studies on ethanol extractive fermentation. Dua, Bozinis, and Pistikopoulos (2002) proposed novel approaches for multiparametric mixed-integer quadratic models through the decomposition into a multiparametric quadratic MIQP model for the upper bound and a potentially nonconvex MINLP model for the lower bound, suggested ways of addressing the nonconvexity in the MINLP, and generated envelopes of parametric solutions and the enclosure of the multiparametric MIQP. Sahinidis, Tawarmalani, and Yu (2003) revisited the design of alternative refrigerants problem, introduced an integer formulation for previously described structural constraints, proposed new structural constraints between one-bonded and higher-bonded groups in the absence of rings and new clique constraints for rings, applied a branch-and-reduce global optimization algorithm with a modification so as to generate all feasible integer solutions, and generated new compounds for refrigerants.…”

Model predictive control of discrete-time hybrid systems with discrete inputs

“…By applying multiparametric programming [14,8,10,11], where the current (initial) state x(k|k) is considered as a parameter, the explicit form of the optimal state feedback u(x(k|k)) of the problem (6) can be obtained. For p = 2 norm the optimization problem is treated as multi-parametric MIQP (mp-MIQP), while for p = 1, ∞ norm the optimization problem can be treated as multi-parametric MILP (mp-MILP).…”