e04ab searches for a minimum, in a given finite interval, of a continuous function of a single variable, using function values only. The method (based on quadratic interpolation) is intended for functions which have a continuous first derivative (although it will usually work if the derivative has occasional discontinuities).

e04bb searches for a minimum, in a given finite interval, of a continuous function of a single variable, using function and first derivative values. The method (based on cubic interpolation) is intended for functions which have a continuous first derivative (although it will usually work if the derivative has occasional discontinuities).

e04cb minimizes a general function $F\left(\mathbf{x}\right)$ of $n$ independent variables $\mathbf{x}={\left(x_1,x_2,\dots ,x_n\right)}^{\mathrm{T}}$ by the Nelder and Mead simplex method (see Nelder and Mead (1965)). Derivatives of the function need not be supplied.

Auxiliary for use as a delegate parameter

e04dg minimizes an unconstrained nonlinear function of several variables using a pre-conditioned, limited memory quasi-Newton conjugate gradient method. First derivatives (or an ‘acceptable’ finite difference approximation to them) are required. It is intended for use on large scale problems.

e04fc is a comprehensive algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. No derivatives are required.

The method is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

Auxiliary for use as a delegate parameter

e04fy is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. No derivatives are required.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04gd is a comprehensive modified Gauss–Newton algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. First derivatives are required.

The method is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04gy is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. First derivatives are required.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04gz is an easy-to-use modified Gauss–Newton algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. First derivatives are required.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04hc checks that a method for evaluating an objective function and its first derivatives produces derivative values which are consistent with the function values calculated.

e04hd checks that a method for calculating second derivatives of an objective function is consistent with a method for calculating the corresponding first derivatives.

e04he is a comprehensive modified Gauss–Newton algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. First and second derivatives are required.

The method is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04hy is an easy-to-use modified Gauss–Newton algorithm for finding an unconstrained minimum of a sum of squares of $m$ nonlinear functions in $n$ variables $\left(m\ge n\right)$. First and second derivatives are required.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04jc is an easy-to-use algorithm that uses methods of quadratic approximation to find a minimum of an objective function $F$ over $\mathbf{x}\in R^n$, subject to fixed lower and upper bounds on the independent variables $x_1,x_2,\dots ,x_n$. Derivatives of $F$ are not required.

The method is intended for functions that are continuous and that have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities). Efficiency is maintained for large $n$.

Auxiliary for use as a delegate parameter

e04jy is an easy-to-use quasi-Newton algorithm for finding a minimum of a function $F\left(x_1,x_2,\dots ,x_n\right)$, subject to fixed upper and lower bounds of the independent variables $x_1,x_2,\dots ,x_n$, using function values only.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04kd is a comprehensive modified Newton algorithm for finding:

• – an unconstrained minimum of a function of several variables;
• – a minimum of a function of several variables subject to fixed upper and/or lower bounds on the variables.

First derivatives are required. The method is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04ky is an easy-to-use quasi-Newton algorithm for finding a minimum of a function $F\left(x_1,x_2,\dots ,x_n\right)$, subject to fixed upper and lower bounds on the independent variables $x_1,x_2,\dots ,x_n$, when first derivatives of $F$ are available.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04kz is an easy-to-use modified Newton algorithm for finding a minimum of a function $F\left(x_1,x_2,\dots ,x_n\right)$, subject to fixed upper and lower bounds on the independent variables $x_1,x_2,\dots ,x_n$, when first derivatives of $F$ are available. It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04lb is a comprehensive modified Newton algorithm for finding:

• an unconstrained minimum of a function of several variables
• a minimum of a function of several variables subject to fixed upper and/or lower bounds on the variables.

First and second derivatives are required. The method is intended for functions which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04ly is an easy-to-use modified-Newton algorithm for finding a minimum of a function, $F\left(x_1,x_2,\dots ,x_n\right)$ subject to fixed upper and lower bounds on the independent variables, $x_1,x_2,\dots ,x_n$ when first and second derivatives of $F$ are available. It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

e04mf solves general linear programming problems. It is not intended for large sparse problems.

e04nc solves linearly constrained linear least squares problems and convex quadratic programming problems. It is not intended for large sparse problems.

e04nf solves general quadratic programming problems. It is not intended for large sparse problems.

Auxiliary for use as a delegate parameter

e04nk solves sparse linear programming or convex quadratic programming problems.

Auxiliary for use as a delegate parameter

e04nq solves sparse linear programming or convex quadratic programming problems. The initialization method (E04NPF not in this release) must have been called before calling e04nq.

Auxiliary for use as a delegate parameter

e04pc solves a linear least squares problem subject to fixed lower and upper bounds on the variables.

e04uc is designed to minimize an arbitrary smooth function subject to constraints (which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints) using a sequential quadratic programming (SQP) method. As many first derivatives as possible should be supplied by you; any unspecified derivatives are approximated by finite differences. It is not intended for large sparse problems.

e04uc may also be used for unconstrained, bound-constrained and linearly constrained optimization.

e04uc uses forward communication for evaluating the objective function, the nonlinear constraint functions, and any of their derivatives.

Auxiliary for use as a delegate parameter

e04uf is designed to minimize an arbitrary smooth function subject to constraints (which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints) using a sequential quadratic programming (SQP) method. You should supply as many first derivatives as possible; any unspecified derivatives are approximated by finite differences. It is not intended for large sparse problems.

e04uf may also be used for unconstrained, bound-constrained and linearly constrained optimization.

e04uf uses reverse communication for evaluating the objective function, the nonlinear constraint functions and any of their derivatives.

e04ug solves sparse nonlinear programming problems.

Auxiliary for use as a delegate parameter

Auxiliary for use as a delegate parameter

e04us is designed to minimize an arbitrary smooth sum of squares function subject to constraints (which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints) using a sequential quadratic programming (SQP) method. As many first derivatives as possible should be supplied by you; any unspecified derivatives are approximated by finite differences. See the description of the optional parameter Derivative Level, in [Description of the Optional Parameters]. It is not intended for large sparse problems.

e04us may also be used for unconstrained, bound-constrained and linearly constrained optimization.

e04vh solves sparse linear and nonlinear programming problems.

e04vj may be used before e04vh to determine the sparsity pattern for the Jacobian.

e04wd is designed to minimize an arbitrary smooth function subject to constraints (which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints) using a sequential quadratic programming (SQP) method. As many first derivatives as possible should be supplied by you; any unspecified derivatives are approximated by finite differences. It is not intended for large sparse problems.

e04wd may also be used for unconstrained, bound-constrained and linearly constrained optimization.

e04wd uses forward communication for evaluating the objective function, the nonlinear constraint functions, and any of their derivatives.

The initialization method (E04WCF not in this release) must have been called before to calling e04wd.

Auxiliary for use as a delegate parameter

e04xa computes an approximation to the gradient vector and/or the Hessian matrix for use in conjunction with, or following the use of an optimization method (such as e04uf).

e04ya checks that a user-supplied method for evaluating a vector of functions and the matrix of their first derivatives produces derivative values which are consistent with the function values calculated.

e04yb checks that a user-supplied method for evaluating the second derivative term of the Hessian matrix of a sum of squares is consistent with a user-supplied method for calculating the corresponding first derivatives.