MINOS is an established choice for both linear and nonlinear optimization problems. It incorporates proven methods for large-scale sparse nonlinear constraints, and its methods are especially effective for nonlinear objectives subject to linear and near-linear constraints.
Developer: Stanford Systems Optimization Laboratory
Current version: 5.51
Problem types supported: Linear, quadratic, and smooth nonlinear objectives and constraints in continuous variables.
Algorithms available: Primal simplex for linear problems; reduced gradient for nonlinear objectives; projected augmented Lagrangian for nonlinear constraints.
Special features: Linear constraints are handled separately from nonlinear ones, for greater efficiency.
Systems Optimization Laboratory website
Guide and option listing: Using AMPL/MINOS