Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems

TLDR: Novel theoretical and algorithmic developments for the solution of mixed- integer optimization problems involving uncertainty are presented, which can be posed as multiparametric mixed-integer optimization models, where uncertainty is described by a set of parameters bounded between lower and upper bounds.

Abstract: In this paper we present novel theoretical and algorithmic developments for the solution of mixed-integer optimization problems involving uncertainty, which can be posed as multiparametric mixed-integer optimization models, where uncertainty is described by a set of parameters bounded between lower and upper bounds. In particular, we address convex nonlinear formulations involving (i) 0−1 integer variables and (ii) uncertain parameters appearing linearly and separately and present on the right-hand side of the constraints. The developments reported in this work are based upon decomposition principles where the problem is decomposed into two iteratively converging subproblems:  (i) a primal and (ii) a master subproblem, representing valid parametric upper and lower bounds on the final solution, respectively. The primal subproblem is formulated by fixing the integer variables which results in a multiparametric nonlinear programming (mp-NLP) problem, which is solved by outer-approximating the nonlinear funct...