optimization solver

今天在測試J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra, "Efficient projections onto the l 1-ball for learning in high dimensions," in  Proceedings of the 25th international conference on Machine learning, 2008, pp. 272-279.

這篇論文中的projection in simplex演算法，將該算法的結果，與直接用pyomo求解比較，該問題是quadratic programming(因為objective function is to minimize Euclidean distance between original vector and projected vector, 而constraint為convex set)。

使用pyomo求解時，solver使用了cplex, gurobi, and ipopt三種，cplex, gurobi與algorithm的結果一致，而使用ipopt時，答案居然有很大的誤差，看來商用軟體還是比較穩定。