| Linear programming (LP), |
| dense, |
| active-set method/primal simplex, |
| alternative 1 | e04mfc |
| alternative 2 | e04ncc |
| sparse, |
| interior point method (IPM) | e04mtc |
| simplex | e04mkc |
| active-set method/primal simplex, |
| recommended (see Section 4.3 in the E04 Chapter Introduction) | e04nqc |
| alternative | e04nkc |
| Quadratic programming (QP), |
| dense, |
| active-set method for (possibly nonconvex) QP problem | e04nfc |
| active-set method for convex QP problem | e04ncc |
| sparse, |
| active-set method sparse convex QP problem, |
| recommended (see Section 4.3 in the E04 Chapter Introduction) | e04nqc |
| alternative | e04nkc |
| interior point method (IPM) for (possibly nonconvex) QP problems | e04stc |
| Second-order Cone Programming (SOCP), |
| dense or sparse, |
| interior point method | e04ptc |
| Semidefinite programming (SDP), |
| generalized augmented Lagrangian method for SDP and SDP with bilinear matrix inequalities (BMI-SDP) | e04svc |
| Nonlinear programming (NLP), |
| dense, |
| active-set sequential quadratic programming (SQP), |
| direct communication, |
| recommended (see Section 4.3 in the E04 Chapter Introduction) | e04ucc |
| alternative | e04wdc |
| reverse communication | e04ufc |
| sparse, |
| active-set sequential quadratic programming (SQP) | e04src |
| interior point method (IPM) | e04stc |
| active-set sequential quadratic programming (SQP), |
| alternative | e04vhc |
| alternative | e04ugc |
| Nonlinear programming (NLP) – derivative-free optimization (DFO), |
| model-based method for bound-constrained optimization | e04jcc |
| model-based method for bound-constrained optimization, |
| reverse communication | e04jec |
| direct communication | e04jdc |
| Nelder–Mead simplex method for unconstrained optimization | e04cbc |
| Nonlinear programming (NLP) – special cases, |
| unidimensional optimization (one-dimensional) with bound constraints, |
| method based on quadratic interpolation, no derivatives | e04abc |
| method based on cubic interpolation | e04bbc |
| unconstrained, |
| preconditioned conjugate gradient method | e04dgc |
| bound-constrained, |
| first order active-set method (nonlinear conjugate gradient) | e04kfc |
| quasi-Newton algorithm, first derivatives | e04kbc |
| modified Newton algorithm, first and second derivatives | e04lbc |
| Nonlinear programming (NLP) – global optimization, |
| bound constrained, |
| branching algorithm, multi-level coordinate search | e05kbc |
| branching algorithm, multi-level coordinate search (D) | e05jbc |
| heuristic algorithm, particle swarm optimization (PSO) | e05sac |
| generic, including nonlinearly constrained, |
| heuristic algorithm, particle swarm optimization (PSO) | e05sbc |
| multi-start | e05ucc |
| Linear least squares, linear regression, data fitting, |
| constrained, |
| bound-constrained least squares problem | e04pcc |
| linearly-constrained active-set method | e04ncc |
| Data fitting, |
| general loss functions (for sum of squares, see nonlinear least squares) | e04gnc |
| Nonlinear least squares, data fitting, |
| unconstrained, |
| combined Gauss–Newton and modified Newton algorithm, |
| no derivatives | e04fcc |
| combined Gauss–Newton and quasi-Newton algorithm, |
| first derivatives | e04gbc |
| covariance matrix for nonlinear least squares problem (unconstrained) | e04ycc |
| constrained, |
| nonlinear constraints active-set sequential quadratic programming (SQP) | e04unc |
| bound constrained, |
| model-based derivative-free algorithm, |
| direct communication | e04ffc |
| reverse communication | e04fgc |
| trust region algorithm, |
| first derivatives, optionally second derivatives | e04ggc |
| Nonlinear least squares, data fitting – global optimization, |
| generic, including nonlinearly constrained, |
| multi-start | e05usc |
| Mixed integer linear programming (MILP), |
| dense, |
| branch and bound method | h02bbc |
| large-scale, |
| branch and bound method | h02bkc |
| Mixed integer nonlinear programming (MINLP), |
| dense, |
| mixed integer sequential quadratic programming (MISQP) | h02dac |
| Operations Research (OR), |
| feature selection, |
| best subset of given size, |
| direct communication | h05abc |
| reverse communication | h05aac |
| transportation problem | h03abc |
| travelling salesman problem, simulated annealing | h03bbc |