To set up a nonlinear optimization problem for solution, first decide between a problem-based approach and solver-based approach. See First Choose Problem-Based or Solver-Based Approach.
For problem-based nonlinear examples and theory, see Problem-Based Nonlinear Optimization.
For solver-based nonlinear examples and theory, see Solver-Based Nonlinear Optimization.
For optimizing multiple objective functions, see Multiobjective Optimization.