W. Adams and H. Sherali, "Mixed-integer bilinear programming prob- lems," Mathematical Programming, vol. 59, no. 1-3, pp. 279-305, March 1993.W.P. Adams and H.D. Sherali, "Mixed-Integer Bilinear Programming Problems," Mathematical Programming, 59(3): 279-305, 1993....
bilinear problems, McCormick envelopes, binary expansion, cutting planes, mixed integer programming AMS subject classifications. 1. Introduction. Consider the mixed integer bilinear program given as min ˆ x T Q 0 ˆ y +f T 0 ˆ x +g...
We study the facet defining inequalities of the convex hull of a mixed-integer bilinear covering arising in trim-loss (or cutting stock) problem under the framework of disjunctive cuts. We show that all of them can be derived using a disjunctive procedure. Some of these are split cuts of ...
Zeng, B., An, Y., Kuznia, L.: Chance constrained mixed integer program: Bilinear and linear formulations, and Benders decomposition. Optimization Online. 2014.B. Zeng, Y. An, and K. Ludwig, "Chance constrained mixed integer program: Bilinear and linear formulations, and benders decomposition,...
Non-ConvexMixed-IntegerNonlinearProgramming:ASurveySamuelBurer∗AdamN.Letchford†28thFebruary2012AbstractAwiderangeofproblemsarising..
or cutting planes. These linearized problems are then solved with an mixed-integer linear programming (MILP) solver such as CPLEX, Gurobi or Cbc. If CPLEX or Gurobi is used, the subproblems can also include quadratic and bilinear nonlinearities directly; then MIQP or MIQCQP subproblems are ...
The case of bilinear bilevel problems is discussed in Section 4, where we focus on pricing problems and Stackelberg games. In Section 5, we then turn to bilevel problems with mixed-integer (non)linear lower-level problems. Also for these problems, we first focus on general properties before...
Then, the corresponding bilinear programming (BLP) problem requires a relaxation on the bilinear Solution algorithm The MILP problem can be solved efficiently by various optimization routines, e.g., CPLEX solver. The VI constraints in Eq. (31) are defined from a set of all extreme points (S)...
mixed-integer nonlinear programmingglobal optimizationprimal heuristicsportfolios of relaxationsThis work considers the global optimization of general non-convex nonlinear and mixed-integer nonlinear programming MINLP problems with underlying bilinear substructures. We combine reformulation–linearization techniques and...
McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constr...