Construction of problems with known global solutions is important for the computational testing of constrained global minimization algorithms. In this paper, it is shown how to construct a concave quadratic function which attains its global minimum at a specified vertex of a polytope in Rn+k. The constructed function is strictly concave in the variables x ∈Rn and is linear in the variables y ∈Rk. The number of linear variables k may be much larger than n, so that large-scale global minimization test problems can be constructed by the methods described here.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
- Global optimization
- concave minimization
- test problems