An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Decomposition in general mathematical programming
Mathematical Programming: Series A and B
An improved branch and bound algorithm for mixed integer nonlinear programs
Computers and Operations Research
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
Computers and Operations Research
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
A Trust-Region Approach to Nonlinear Systems of Equalities and Inequalities
SIAM Journal on Optimization
Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation
Computational Optimization and Applications
Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm
Computational Optimization and Applications
A heuristic for the label printing problem
Computers and Operations Research
Solving a dynamic separation problem using MINLP techniques
Applied Numerical Mathematics
Global optimization of signomial mixed-integer nonlinear programming problems with free variables
Journal of Global Optimization
A dynamic convexized method for nonconvex mixed integer nonlinear programming
Computers and Operations Research
Heuristics for convex mixed integer nonlinear programs
Computational Optimization and Applications
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
A local relaxation method for the cardinality constrained portfolio optimization problem
Computational Optimization and Applications
On branching rules for convex mixed-integer nonlinear optimization
Journal of Experimental Algorithmics (JEA)
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This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems.In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver.A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed.