Everyone has something they would like to minimize or maximize. Mathematical models and computer implementations give us the field of numerical optimization. Constraints reflecting physical reality require numerical linear algebra.
We review some of the software and aerospace applications associated with Philip Gill's contributions to numerical optimization. We then review the iterative methods CG, SYMMLQ, and MINRES for solving symmetric Ax=b and show how SYMMLQ provides bounds on the 2-norm of the error for CG iterates.