New advances in the GOP algorithm for global optimization
- Princeton, NJ (United States)
Floudas and Visweswaran proposed a deterministic global optimization algorithm (GOP) for solving certain classes of nonconvex optimization problems through a series of primal and relaxed dual problems that provide valid lower and upper bounds respectively on the global solution. The algorithm was proved to have finite convergence to an {epsilon}-global optimum. This work presents this algorithm in a branch-and-bound framework, and proposed several new reduction tests that can be incorporated at each node. These tests help to prune the tree and provide tighter underestimators for the dual problems. We also present a mixed-integer linear programming (MILP) formulation for the dual problem, which enables an implicit enumeration of the nodes in the branch-and-bound tree at each iteration. Finally, a new partitioning scheme is proposed that enables the solution of the dual problem at each iteration through a linear number of subproblems. Simple examples are presented to help illustrate the reduction properties as well as the two new approaches for solving the dual problems.
- OSTI ID:
- 36016
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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