Bifurcation problems in nonlinear parametric programming
Mathematical Programming: Series A and B
Generalized convexity and concavity of the optimal value function in nonlinear programming
Mathematical Programming: Series A and B
Computable bounds on parametric solutions of convex problems
Mathematical Programming: Series A and B
Global Optimization Issues in Multiparametric Continuous and Mixed-Integer Optimization Problems
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Parametric global optimisation for bilevel programming
Journal of Global Optimization
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions
Automatica (Journal of IFAC)
Dynamic programming for constrained optimal control of discrete-time linear hybrid systems
Automatica (Journal of IFAC)
Design of robust model-based controllers via parametric programming
Automatica (Journal of IFAC)
On the global solution of multi-parametric mixed integer linear programming problems
Journal of Global Optimization
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In this paper, we present a novel global optimisation approach for the general solution of multi-parametric mixed integer linear programs (mp-MILPs). We describe an optimisation procedure which iterates between a (master) mixed integer nonlinear program and a (slave) multi-parametric program. Moreover, we explain how to overcome the presence of bilinearities, responsible for the non-convexity of the multi-parametric program, in two classes of mp-MILPs, with (i) varying parameters in the objective function and (ii) simultaneous presence of varying parameters in the objective function and the right-hand side of the constraints. Examples are provided to illustrate the solution steps.