| Linear programming (LP), |
| dense, |
| active-set method/primal simplex, |
| alternative 1 | e04mff |
| alternative 2 | e04ncf |
| sparse, |
| interior point method (IPM) | e04mtf |
| active-set method/primal simplex, |
| recommended (see Section 3.3 in the E04 Chapter Introduction) | e04nqf |
| alternative | e04nkf |
| Quadratic programming (QP), |
| dense, |
| active-set method for (possibly nonconvex) QP problem | e04nff |
| active-set method for convex QP problem | e04ncf |
| sparse, |
| active-set method sparse convex QP problem, |
| recommended (see Section 3.3 in the E04 Chapter Introduction) | e04nqf |
| alternative | e04nkf |
| interior point method (IPM) for (possibly nonconvex) QP problems | e04stf |
| Second-order Cone Programming (SOCP), |
| dense or sparse, |
| interior point method | e04ptf |
| Semidefinite programming (SDP), |
| generalized augmented Lagrangian method for SDP and SDP with bilinear matrix inequalities (BMI-SDP) | e04svf |
| Nonlinear programming (NLP), |
| dense, |
| active-set sequential quadratic programming (SQP), |
| direct communication, |
| recommended (see Section 3.3 in the E04 Chapter Introduction) | e04ucf |
| alternative | e04wdf |
| reverse communication | e04uff |
| sparse, |
| active-set sequential quadratic programming (SQP) | e04srf |
| interior point method (IPM) | e04stf |
| active-set sequential quadratic programming (SQP), |
| alternative | e04vhf |
| alternative | e04ugf |
| Nonlinear programming (NLP) – derivative-free optimization (DFO), |
| model-based method for bound-constrained optimization | e04jcf |
| model-based method for bound-constrained optimization, |
| reverse communication | e04jef |
| direct communication | e04jdf |
| Nelder–Mead simplex method for unconstrained optimization | e04cbf |
| Nonlinear programming (NLP) – special cases, |
| unidimensional optimization (one-dimensional) with bound constraints, |
| method based on quadratic interpolation, no derivatives | e04abf |
| method based on cubic interpolation | e04bbf |
| unconstrained, |
| preconditioned conjugate gradient method | e04dgf |
| bound-constrained, |
| first order active-set method (nonlinear conjugate gradient) | e04kff |
| quasi-Newton algorithm, no derivatives | e04jyf |
| quasi-Newton algorithm, first derivatives | e04kyf |
| modified Newton algorithm, first derivatives | e04kdf |
| modified Newton algorithm, first derivatives, easy-to-use | e04kzf |
| modified Newton algorithm, first and second derivatives | e04lbf |
| modified Newton algorithm, first and second derivatives, easy-to-use | e04lyf |
| Nonlinear programming (NLP) – global optimization, |
| bound constrained, |
| branching algorithm, multi-level coordinate search | e05kbf |
| branching algorithm, multi-level coordinate search (D) | e05jbf |
| heuristic algorithm, particle swarm optimization (PSO) | e05saf |
| generic, including nonlinearly constrained, |
| heuristic algorithm, particle swarm optimization (PSO) | e05sbf |
| multi-start | e05ucf |
| Linear least squares, linear regression, data fitting, |
| constrained, |
| bound-constrained least squares problem | e04pcf |
| linearly-constrained active-set method | e04ncf |
| Data fitting, |
| general loss functions (for sum of squares, see nonlinear least squares) | e04gnf |
| Nonlinear least squares, data fitting, |
| unconstrained, |
| combined Gauss–Newton and modified Newton algorithm, |
| no derivatives | e04fcf |
| no derivatives, easy-to-use | e04fyf |
| first derivatives | e04gdf |
| first derivatives, easy-to-use | e04gzf |
| first and second derivatives | e04hef |
| first and second derivatives, easy-to-use | e04hyf |
| combined Gauss–Newton and quasi-Newton algorithm, |
| first derivatives | e04gbf |
| first derivatives, easy-to-use | e04gyf |
| covariance matrix for nonlinear least squares problem (unconstrained) | e04ycf |
| bound constrained, |
| model-based derivative-free algorithm, |
| direct communication | e04fff |
| reverse communication | e04fgf |
| trust region algorithm, |
| first derivatives, optionally second derivatives | e04ggf |
| generic, including nonlinearly constrained, |
| nonlinear constraints active-set sequential quadratic programming (SQP) | e04usf |
| Nonlinear least squares, data fitting – global optimization, |
| generic, including nonlinearly constrained, |
| multi-start | e05usf |
| Mixed integer linear programming (MILP), |
| dense, |
| branch and bound method | h02bbf |
| sparse, |
| branch and bound method | h02cef |
| Mixed integer quadratic programming (MIQP), |
| dense, |
| branch and bound method | h02cbf |
| sparse, |
| branch and bound method | h02cef |
| Mixed integer nonlinear programming (MINLP), |
| dense, |
| mixed integer sequential quadratic programming (MISQP) | h02daf |
| Operations Research (OR), |
| feature selection, |
| best subset of given size, |
| direct communication | h05abf |
| reverse communication | h05aaf |
| shortest path through directed or undirected network | h03adf |
| transportation problem | h03abf |
| travelling salesman problem, simulated annealing | h03bbf |