Andrew R. Conn, L.N. Vicente
Optimization Methods and Software
Could continuous optimization address efficiently logical constraints? We propose a continuous-optimization alternative to the usual discrete-optimization (big-M and complementary) formulations of logical constraints, that can lead to effective practical methods. Based on the simple idea of guiding the search of a continuous-optimization descent method towards the parts of the domain where the logical constraint is satisfied, we introduce a smooth penalty-function formulation of logical constraints, and related theoretical results. This formulation allows a direct use of state-of-the-art continuous optimization solvers. The effectiveness of the continuous quadrant penalty formulation is demonstrated on an aircraft conflict avoidance application.
Andrew R. Conn, L.N. Vicente
Optimization Methods and Software
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Discrete Optimization
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Future Generation Computer Systems
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IMA Journal of Numerical Analysis