Mathematical Programming Submit manuscript Amitabh Basu, Michele Conforti, Marco Di Summa & Hongyi Jiang 1296 Accesses Explore all metrics Abstract We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we ...
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that...
In the history of integer programming, the basic branch-and-bound method has been extended to the so-called branch-and-cut (B&C) method. This means that, besides branching, additional valid inequalities or cuts are introduced at the nodes of the branch-and-bound tree to tighten the formulatio...
From this expression, we will determine the sets of constraints to define a Mixed-Integer Linear Programming (MILP) formulation for the Multidimensional Multi-Way Number Partitioning Problem (MDMWNPP). Let y∈R+ be the diameter to be minimized. Then, using the property:(2)maxi,j∈Inai-aj=...
Integer Programming and Combinatorial Optimization: proceedingsG. Cornuejols and Y. Li. On the rank of mixed 0-1 polyhedra. In K. Aardal and A.M.H. Gerards, eds., IPCO 2001, Lecture Notes in Computer Science, 2081:71{77, 2001....
Mixed-integer programmingPRIDEWe focus on extending the applicability of the mixed-integer programming (MIP) based method in differential cryptanalysis such that more work can be done automatically. Firstly, we show how to use the MIP-based technique to obtain almost all high probability 2-round ...
Already trained neural networks and mixed integer linear programming have been brought successfully together in the past. Note, that this work is focussing on the direct optimization of the network weights and its parameters from training data with a close connection to the works presented in Section...
The next algorithm follows a dynamic programming approach (recall that Δ1(T) is the maximum degree of T): Proposition 8 If Δ1 is a fixed integer, then the problem STRICT COLORING can be solved in polynomial time for mixed hypertrees with maximum vertex degree at most Δ1. Moreover, ...
A relax-and-cut framework for gomory's mixed-integer cuts. In Andrea Lodi, Michela Milano, and Paolo Toth, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, volume 6140 of Lecture Notes in Computer Science, pages 123-135. Springer ...
Our work can be seen as a third proposal for finding rank-1 GMI cuts. We also note that the sa...Matteo Fischetti and Domenico Salvagnin. A relax-and-cut framework for gomory's mixed-integer cuts. Mathematical Programming Computation, 3:79-102, 2011....