As you point out in [2], it would be more correct to say that among the optimal solutions there is always one at a vertex of the polyhedron</nitpicking>
Also, simplex methods are very versatile when combined with other methods (see branch-and-bound for mixed integer linear optimization), but are sometimes easily beaten by barrier methods.
Excellent textbooks for LP: Chvátal [4] and Bertsimas and Tsitsiklis [5]. For mixed integer linear optimization: Wolsey [6], Nemhauser and Wolsey [7], and Conforti et al. [8].
[4] V. Chvátal, Linear Programming. MacMillan 1983.
[5] D. Bertsimas, J.N. Tsitsiklis. Introduction to linear optimization. Vol. 6. Belmont, MA: Athena Scientific, 1997.
As you point out in [2], it would be more correct to say that among the optimal solutions there is always one at a vertex of the polyhedron</nitpicking>
Also, simplex methods are very versatile when combined with other methods (see branch-and-bound for mixed integer linear optimization), but are sometimes easily beaten by barrier methods.
Excellent textbooks for LP: Chvátal [4] and Bertsimas and Tsitsiklis [5]. For mixed integer linear optimization: Wolsey [6], Nemhauser and Wolsey [7], and Conforti et al. [8].
[4] V. Chvátal, Linear Programming. MacMillan 1983.
[5] D. Bertsimas, J.N. Tsitsiklis. Introduction to linear optimization. Vol. 6. Belmont, MA: Athena Scientific, 1997.
[6] L.A. Wolsey (1998). Integer programming (Vol. 42). New York: Wiley.
[7] L.A. Wolsey, G.L. Nemhauser. Integer and combinatorial optimization. John Wiley & Sons; 2014 Aug 28.
[8] M. Conforti, G. Cornuéjols, G. Zambelli (2014). Integer programming (Vol. 271). Berlin: Springer.