Sufficient
conditions are given for any local minimum of a function of two integer
variables to be a global minimum. An example is given to show that
a function of two integer variables need not be discrete convex for this
condition to hold.
References
[1]
Tovey, C. (2002) Tutorial on Computational Complexity. Interfaces, 32, 30-61. https://doi.org/10.1287/inte.32.3.30.39
[2]
Bazaraa, M., Sherali, H. and Shetty, C. (1993) Nonlinear Programming, Theory and Algorithms. John Wiley & Sons, New York.
[3]
Kumin, H. (1973) On Characterizing the Minimum of a Function of Two Variables, One of Which Is Discrete. Management Science, 20, 126-129. https://doi.org/10.1287/mnsc.20.1.126
[4]
Ponstein, J. (1967) Seven Kinds of Convexity. SIAM Review, 9, 115-119. https://doi.org/10.1137/1009007
[5]
Yüceer, U. (2002) Discrete Convexity: Convexity for Functions Defined on Discrete Spaces. Discrete Applied Mathematics, 119, 297-304. https://doi.org/10.1016/S0166-218X(01)00191-3
