Laurence A. Wolsey

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Let N be a finite set and z be a real-valued function defined on the set of subsets of N that satisfies z(S)+z(T)>-z(SUT)+z(SnT) for all S, T in N. Such a function is called submodular. We consider the problem maXscN {z(S): IS[ <-K, z(S) submodular}. Several hard combinatorial optimization problems can be posed in this framework. For example, the problem of(More)
A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of “strong” valid inequalities for specific models and computationally gives results as good as or better than those obtained from several existing separation routines including flow cover and integer cover inequalities. The heuristic is(More)
Constraints arising in practice often contain many 0-1 variables and one or a small number of continuous variables. Existing knapsack separation routines cannot be used on such constraints. Here we study such constraint sets, and derive valid inequalities that can be used as cuts for such sets, as well for more general mixed 0-1 constraints. Specifically we(More)
l ; ~ x ; ~ l . l j , j ~ . M I , I]yj<-xj<-u~yj, j~M2, yje {o, 1}, jeM2UM3. where x~, yj are variables, aj, bj, d, l], u~ are constants, and M1, M2, M3 are sets (M2 • p t / ~ t and M3 need not be disjoint)• The constraints xj_ u.i, xj_ ujyi are called simple and variable (VUB) upper bound constraints respectively, and lower bound constraints are defined(More)