Convexification of classes of mixed-integer sets with L♮-convexity
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(Mixed) Integer Nonlinear Programming
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Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more
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For mixed-integer programs (MIPs), strong branching is a highly effective variable selection method to reduce the number of nodes in the branch-and-bound algorithm. Extending it to nonlinear problems is conceptually simple but practically limited. Branching on a binary variable fixes the variable to 0 or 1, whereas branching on a continuous variable requires an additional … Read more
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We present the architecture and central parts of the FICO Xpress Global optimization solver. In particular, we focus on how we built a global solver for the general class of mixed-integer nonlinear optimization problems by combining and extending two existing components of the FICO Xpress Solver, namely the mixed-integer linear optimization solver and the successive … Read more