To solve an optimization problem with bound constraints. More...

#include <OptSolver.h>

Public Types
enum	OptMethod { GRADIENT = 0 , TRUNCATED_NEWTON = 1 , SIMULATED_ANNEALING = 2 , NELDER_MEAD = 3 , NEWTON = 4 }
	Choose optimization algorithm. More...

Public Member Functions
	OptSolver ()
	Default constructor.

	OptSolver (Vect< real_t > &x)
	Constructor using vector of optimization variables. More...

	OptSolver (MyOpt &opt, Vect< real_t > &x)
	Constructor using vector of optimization variables. More...

	~OptSolver ()
	Destructor.

void	set (Vect< real_t > &x)
	Set Solution vector.

int	getNbFctEval () const
	Return the total number of function evaluations.

void	setOptMethod (OptMethod m)
	Choose optimization method. More...

void	setBC (const Vect< real_t > &bc)
	Prescribe boundary conditions as constraints. More...

void	setObjective (string exp)
	Define the objective function to minimize by an algebraic expression. More...

void	setGradient (string exp, int i=1)
	Define a component of the gradient of the objective function to minimize by an algebraic expression. More...

void	setHessian (string exp, int i=1, int j=1)
	Define an entry of the Hessian matrix. More...

void	setIneqConstraint (string exp, real_t penal=1./OFELI_TOLERANCE)
	Impose an inequatity constraint by a penalty method. More...

void	setEqConstraint (string exp, real_t penal=1./OFELI_TOLERANCE)
	Impose an equatity constraint by a penalty method. More...

void	setObjective (function< real_t(real_t)> f)
	Define the objective function by a user defined one-variable function. More...

void	setObjective (function< real_t(Vect< real_t >)> f)
	Define the objective function by a user defined multi-variable function. More...

void	setGradient (function< real_t(real_t)> f)
	Define the derivative of the objective function by a user defined function. More...

void	setGradient (function< Vect< real_t >(Vect< real_t >)> f)
	Define the gradient of the objective function by a user defined function. More...

void	setOptClass (MyOpt &opt)
	Choose user defined optimization class. More...

void	setLowerBound (size_t i, real_t lb)
	Define lower bound for a particular optimization variable. More...

void	setUpperBound (size_t i, real_t ub)
	Define upper bound for a particular optimization variable. More...

void	setEqBound (size_t i, real_t b)
	Define value to impose to a particular optimization variable. More...

void	setUpperBound (real_t ub)
	Define upper bound for optimization variable. More...

void	setUpperBounds (Vect< real_t > &ub)
	Define upper bounds for optimization variables. More...

void	setLowerBound (real_t lb)
	Define lower bound for optimization variable. More...

void	setLowerBounds (Vect< real_t > &lb)
	Define lower bounds for optimization variables. More...

void	setSAOpt (real_t rt, int ns, int nt, int &neps, int maxevl, real_t t, Vect< real_t > &vm, Vect< real_t > &xopt, real_t &fopt)
	Set Simulated annealing options. More...

void	setTolerance (real_t toler)
	Set error tolerance. More...

void	setMaxIterations (int n)
	Set maximal number of iterations.

int	getNbObjEval () const
	Return number of objective function evaluations.

real_t	getTemperature () const
	Return the final temperature. More...

int	getNbAcc () const
	Return the number of accepted objective function evaluations. More...

int	getNbOutOfBounds () const
	Return the total number of trial function evaluations that would have been out of bounds. More...

real_t	getOptObj () const
	Return Optimal value of the objective.

int	run ()
	Run the optimization algorithm. More...

int	run (real_t toler, int max_it)
	Run the optimization algorithm. More...

real_t	getSolution () const
	Return solution in the case of a one variable optimization. More...

void	getSolution (Vect< real_t > &x) const
	Get solution vector. More...

Detailed Description

To solve an optimization problem with bound constraints.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Member Enumeration Documentation

◆ OptMethod

enum OptMethod

Choose optimization algorithm.

Enumerator
GRADIENT	Gradient method
TRUNCATED_NEWTON	Truncated Newton method
SIMULATED_ANNEALING	Simulated annealing global optimization method
NELDER_MEAD	Nelder-Mead global optimization method
NEWTON	Newton's method

Constructor & Destructor Documentation

◆ OptSolver() [1/2]

OptSolver ( Vect< real_t > & x )

Constructor using vector of optimization variables.

Parameters

[in] x Vector having as size the number of optimization variables. It contains the initial guess for the optimization algorithm.

Remarks: After using the member function run, the vector x contains the obtained solution if the optimization procedure was successful

◆ OptSolver() [2/2]

OptSolver	(	MyOpt &	opt,
		Vect< real_t > &	x
	)

Constructor using vector of optimization variables.

Parameters

[in]	opt	Reference to instance of user defined optimization class. This class inherits from abstract class MyOpt. It must contain the member function `double` `Objective(Vect<double> &x)` which returns the value of the objective for a given solution vector `x`. The user defined class must contain, if the optimization algorithm requires it the member function `Gradient(Vect<double> &x, Vect<double> &g)` which stores the gradient of the objective in the vector `g` for a given optimization vector `x`. The user defined class must also contain, if the optimization algorithm requires it the member function
[in]	x	Vector having as size the number of optimization variables. It contains the initial guess for the optimization algorithm.

Remarks: After using the member function run, the vector x contains the obtained solution if the optimization procedure was successful

Member Function Documentation

◆ getNbAcc()

int getNbAcc ( ) const

Return the number of accepted objective function evaluations.

This function is meaningful only if the Simulated Annealing algorithm is used

◆ getNbOutOfBounds()

int getNbOutOfBounds ( ) const

Return the total number of trial function evaluations that would have been out of bounds.

This function is meaningful only if the Simulated Annealing algorithm is used

◆ getSolution() [1/2]

real_t getSolution ( ) const

Return solution in the case of a one variable optimization.

In the case of a one variable problem, the solution value is returned, if the optimization procedure was successful

◆ getSolution() [2/2]

void getSolution ( Vect< real_t > & x ) const

Get solution vector.

The vector x contains the solution of the optimization problem. Note that if the constructor using an initial vector was used, the vector will contain the solution once the member function run has beed used (If the optimization procedure was successful)

Parameters

[out] x solution vector

◆ getTemperature()

real_t getTemperature ( ) const

Return the final temperature.

This function is meaningful only if the Simulated Annealing algorithm is used

◆ run() [1/2]

int run ( )

Run the optimization algorithm.

This function runs the optimization procedure using default values for parameters. To modify these values, user the function run with arguments

◆ run() [2/2]

int run	(	real_t	toler,
		int	max_it
	)

Run the optimization algorithm.

Parameters

[in]	toler	Tolerance value for convergence testing
[in]	max_it	Maximal number of iterations to achieve convergence

◆ setBC()

void setBC ( const Vect< real_t > & bc )

Prescribe boundary conditions as constraints.

This member function is useful in the case of optimization problems where the optimization variable vector is the solution of a partial differential equation. For this case, Dirichlet boundary conditions can be prescribed as constraints for the optimization problem

Parameters

[in] bc Vector containing the values to impose on degrees of freedom. This vector must have been constructed using the Mesh instance.

Remarks: Only degrees of freedom with positive code are taken into account as prescribed

◆ setEqBound()

void setEqBound	(	size_t	i,
		real_t	b
	)

Define value to impose to a particular optimization variable.

Method to impose a value for a component of the optimization variable

Parameters

[in]	i	Index of component to enforce (index starts from `1` )
[in]	b	Value to impose

◆ setEqConstraint()

void setEqConstraint	(	string	exp,
		real_t	penal = `1./OFELI_TOLERANCE`
	)

Impose an equatity constraint by a penalty method.

The constraint is of the form F(x) = 0 where F is any function of the optimization variable vector v

Parameters

[in]	exp	Regular expression defining the constraint (the function `F`
[in]	penal	Penalty parameter (large number) [Default: `1./DBL_EPSILON`]

◆ setGradient() [1/3]

void setGradient ( function< real_t(real_t)> f )

Define the derivative of the objective function by a user defined function.

Parameters

[in] f Function given as a function of a real variable and returning the derivative of the objective value. This function can be defined by the calling program as a C-function and then cast to an instance of class function

◆ setGradient() [2/3]

void setGradient ( function< Vect< real_t >(Vect< real_t >)> f )

Define the gradient of the objective function by a user defined function.

Parameters

[in] f Function given as a function of a many real variables and returning the partial derivatives of the objective value. This function can be defined by the calling program as a C-function and then cast to an instance of class function

◆ setGradient() [3/3]

void setGradient	(	string	exp,
		int	i = `1`
	)

Define a component of the gradient of the objective function to minimize by an algebraic expression.

Parameters

[in]	exp	Regular expression defining the objective function
[in]	i	Component of gradient [Default: `1`]

◆ setHessian()

void setHessian	(	string	exp,
		int	i = `1`,
		int	j = `1`
	)

Define an entry of the Hessian matrix.

Parameters

[in]	exp	Regular expression defining the Hessian matrix entry
[in]	i	i-th row of Hessian matrix [Default: `1`]
[in]	j	j-th column of Hessian matrix [Default: `1`]

◆ setIneqConstraint()

void setIneqConstraint	(	string	exp,
		real_t	penal = `1./OFELI_TOLERANCE`
	)

Impose an inequatity constraint by a penalty method.

The constraint is of the form F(x) <= 0 where F is any function of the optimization variable vector v

Parameters

[in]	exp	Regular expression defining the constraint (the function `F`
[in]	penal	Penalty parameter (large number) [Default: `1./DBL_EPSILON`]

◆ setLowerBound() [1/2]

void setLowerBound ( real_t lb )

Define lower bound for optimization variable.

Case of a one-variable problem

Parameters

[in] lb Lower value

◆ setLowerBound() [2/2]

void setLowerBound	(	size_t	i,
		real_t	lb
	)

Define lower bound for a particular optimization variable.

Method to impose a lower bound for a component of the optimization variable

Parameters

[in]	i	Index of component to bound (index starts from `1` )
[in]	lb	Lower bound

◆ setLowerBounds()

void setLowerBounds ( Vect< real_t > & lb )

Define lower bounds for optimization variables.

Parameters

[in] lb Vector containing lower values for variables

◆ setObjective() [1/3]

void setObjective ( function< real_t(real_t)> f )

Define the objective function by a user defined one-variable function.

This function can be used in the case where a user defined function is to be given. To be used in the one-variable case.

Parameters

[in] f Function given as a function of one real variable which is the optimization variable and returning the objective value. This function can be defined by the calling program as a C-function and then cast to an instance of class function

◆ setObjective() [2/3]

void setObjective ( function< real_t(Vect< real_t >)> f )

Define the objective function by a user defined multi-variable function.

This function can be used in the case where a user defined function is to be given. To be used in the multivariable case.

Parameters

[in] f Function given as a function of many real variables and returning the objective value. This function can be defined by the calling program as a C-function and then cast to an instance of class function

◆ setObjective() [3/3]

void setObjective ( string exp )

Define the objective function to minimize by an algebraic expression.

Parameters

[in] exp Regular expression defining the objective function

◆ setOptClass()

void setOptClass ( MyOpt & opt )

Choose user defined optimization class.

Parameters

[in] opt Reference to inherited user specified optimization class

◆ setOptMethod()

void setOptMethod ( OptMethod m )

Choose optimization method.

Parameters

[in]

m

Enumerated value to choose the optimization algorithm to use. Must be chosen among the enumerated values:

GRADIENT: Gradient steepest descent method with projection for bounded constrained problems
TRUNCATED_NEWTON: The Nash's Truncated Newton Algorithm, due to S.G. Nash (Newton-type Minimization via the Lanczos method, SIAM J. Numer. Anal. 21 (1984) 770-778).
SIMULATED_ANNEALING: Global optimization simulated annealing method. See Corana et al.'s article: "Minimizing Multimodal Functions of Continuous Variables with the Simulated Annealing Algorithm" in the September 1987 (vol. 13, no. 3, pp. 262-280) issue of the ACM Transactions on Mathematical Software.
NELDER_MEAD: Global optimization Nelder-Mead method due to John Nelder, Roger Mead (A simplex method for function minimization, Computer Journal, Volume 7, 1965, pages 308-313). As implemented by R. ONeill (Algorithm AS 47: Function Minimization Using a Simplex Procedure, Applied Statistics, Volume 20, Number 3, 1971, pages 338-345).

◆ setSAOpt()

void setSAOpt	(	real_t	rt,
		int	ns,
		int	nt,
		int &	neps,
		int	maxevl,
		real_t	t,
		Vect< real_t > &	vm,
		Vect< real_t > &	xopt,
		real_t &	fopt
	)

Set Simulated annealing options.

Remarks: This member function is useful only if simulated annealing is used.

Parameters

[in]	rt	The temperature reduction factor. The value suggested by Corana et al. is .85. See Goffe et al. for more advice.
[in]	ns	Number of cycles. After nsnb_var* function evaluations, each element of vm is adjusted so that approximately half of all function evaluations are accepted. The suggested value is 20.
[in]	nt	Number of iterations before temperature reduction. After ntnsn function evaluations, temperature (t) is changed by the factor rt. Value suggested by Corana et al. is max(100,5nb_var)*. See Goffe et al. for further advice.
[in]	neps	Number of final function values used to decide upon termination. See `eps`. Suggested value is 4
[in]	maxevl	The maximum number of function evaluations. If it is exceeded, the return code=1.
[in]	t	The initial temperature. See Goffe et al. for advice.
[in]	vm	The step length vector. On input it should encompass the region of interest given the starting value x. For point x[i], the next trial point is selected is from x[i]-vm[i] to x[i]+vm[i]. Since vm is adjusted so that about half of all points are accepted, the input value is not very important (i.e. is the value is off, OptimSA adjusts vm to the correct value).
[out]	xopt	optimal values of optimization variables
[out]	fopt	Optimal value of objective

◆ setTolerance()

void setTolerance ( real_t toler )

Set error tolerance.

Parameters

[in] toler Error tolerance for termination. If the final function values from the last neps temperatures differ from the corresponding value at the current temperature by less than eps and the final function value at the current temperature differs from the current optimal function value by less than toler, execution terminates and the value 0 is returned.

◆ setUpperBound() [1/2]

void setUpperBound ( real_t ub )

Define upper bound for optimization variable.

Case of a one-variable problem

Parameters

[in] ub Upper bound

◆ setUpperBound() [2/2]

void setUpperBound	(	size_t	i,
		real_t	ub
	)

Define upper bound for a particular optimization variable.

Method to impose an upper bound for a component of the optimization variable

Parameters

[in]	i	Index of component to bound (index starts from `1` )
[in]	ub	Upper bound

◆ setUpperBounds()

void setUpperBounds ( Vect< real_t > & ub )

Define upper bounds for optimization variables.

Parameters

[in] ub Vector containing upper values for variables

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ OptMethod

Constructor & Destructor Documentation

◆ OptSolver() [1/2]

◆ OptSolver() [2/2]

Member Function Documentation

◆ getNbAcc()

◆ getNbOutOfBounds()

◆ getSolution() [1/2]

◆ getSolution() [2/2]

◆ getTemperature()

◆ run() [1/2]

◆ run() [2/2]

◆ setBC()

◆ setEqBound()

◆ setEqConstraint()

◆ setGradient() [1/3]

◆ setGradient() [2/3]

◆ setGradient() [3/3]

◆ setHessian()

◆ setIneqConstraint()

◆ setLowerBound() [1/2]

◆ setLowerBound() [2/2]

◆ setLowerBounds()

◆ setObjective() [1/3]

◆ setObjective() [2/3]

◆ setObjective() [3/3]

◆ setOptClass()

◆ setOptMethod()

◆ setSAOpt()

◆ setTolerance()

◆ setUpperBound() [1/2]

◆ setUpperBound() [2/2]

◆ setUpperBounds()