Discrete and continuous nonconvex programming problems arise in a host of practical applications in the context of production, location-allocation, distribution, economics and game theory, process design, and engineering design situations. Several recent advances have been made in the development of branch-and-cut algorithms for discrete optimization problems and in polyhedral outer-approximation methods for continuous nonconvex programming problems. At the heart of these approaches is a sequence of linear programming problems that drive the solution process. The success of such algorithms is strongly linked to the strength or tightness of the linear programming representations employed.
KeywordsProgramming Problem Valid Inequality Linear Programming Relaxation Subgradient Method Continuous Relaxation
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