NAG FL Interface
Optimization

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This selection provides a list of routines from the NAG Library for solving various mathematical optimization problems ordered by the problem type. It spans across Chapters E04, E05 and H. Please refer to the E04, E05 and H Chapter Introductions for help with the problem type classification, algorithmic details and advice on the selection of the right solver. See the full chapter tables of contents as listed above for additional functionality not listed here, such as file I/O or option setting routines.
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