global optimisation problem, and therefore likely to be NP-hard (see, e.g., [118, 124]). In fact, the situation is worse than this. Several simple cases of non-convex MINLP, including the case in which all functions are quadratic, all variables are integer-constrained, and the number ...
We identify for which type of mixed integer non-linear problems our method can be applied efficiently, derive several bounding operations and analyze their rates of convergence theoretically. Moreover, we show that the accuracy of any algorithm for solving the problem with fixed integer variables ...
development for global optimization of nonconvex MINLP problems (Grossmann & Daichendt, 1996; Ad- jiman, Androulakis & Floudas, 1997). For gas membrane separation systems, a major difficulty in developing MINLP synthesis techniques is that fundamental permeator models are comprised of differentia...
We call (MOMIP) a multiobjective mixed-integer convex optimization problem if all involved functions \(f_i, i \in [p]\) and \(g_j, j \in [q]\) are convex. Otherwise, we call it a multiobjective mixed-integer nonconvex optimization problem. Obviously, for \(m=0\) and for \(n...
(SQP) stabilised by using trust regions. It can deal with both convex and nonconvex problems and problems with possibly expensive function evaluations. In addition, it is not assumed that the mixed integer problem has to be relaxable; the function evaluations are requested only at integral points...
Mixed integer programming
do not change drastically when in- or decrementing an integer variable, successive quadratic approximations are applied. It is not assumed that integer variables are relaxable, i.e., problem functions are evaluated only at integer points. The code is applicable also to nonconvex optimization ...
In [35], a new method based on a nonmonotone linesearch and primitive directions is proposed to solve a more general problem where the objective function is allowed to be nonconvex. The primitive directions allow the algorithm to escape bad local minima, thus providing the potential to find a...
过程综合的混合整数非线性规划嵌套式求解方法[D】. 15 Fletdher K sonWa叫.Dundce,2008. Leyf|衙S.Ⅻ[N】口BB[computer UⅢ由ed Kingdom:Unive巧ityofDuⅡd∞. 16 Gal肋BGrossm籼I distributed E.oIm盥ldesi印of AnoVel for mixed nonUnear hybridalgorithm solvinginteger problem Lin VVen¨1‘and...
However, KKT-based reformulations are prohibitive when integer variables are present in the lower-level problem. Heuristic techniques have been employed to manage the complexity of non-smooth functions and mixed-integer variables for solving mixed-integer bi-level optimization problems. Nevertheless, ...