An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
An improved branch and bound algorithm for mixed integer nonlinear programs
Computers and Operations Research
Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming
Computational Optimization and Applications
IEEE Computational Science & Engineering
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
MINLPLib--A Collection of Test Models for Mixed-Integer Nonlinear Programming
INFORMS Journal on Computing
Encyclopedia of Optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
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In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.