Combining Progressive Hedging with a Frank-wolfe
نویسندگان
چکیده
We present a new primal-dual algorithm for computing the value of the Lagrangian 6 dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity con7 straints. The algorithm relies on the well-known progressive hedging method, but unlike previous 8 progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal 9 Lagrangian dual value. The key improvement in the new algorithm is an inner loop of optimized 10 linearization steps, similar to those taken in the classical Frank-Wolfe method. Numerical results 11 demonstrate that our new algorithm empirically outperforms the standard implementation of pro12 gressive hedging for obtaining bounds in SMIP. 13
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