solnp2NLP: Solve constrained nonlinear minimization problem
In Rsolnp2: Non-linear Programming with non-linear Constraints

Description Usage Arguments Details Value Author(s) References See Also Examples

Solve constrained nonlinear minimization problem.

solnp2NLP( 
    par, fun,
    par.lower = NULL, par.upper = NULL,   
    eqA = NULL, eqA.bound = NULL,
    ineqA = NULL, ineqA.lower = NULL, ineqA.upper = NULL,  
    eqFun = list(), eqFun.bound = NULL,
    ineqFun = list(), ineqFun.lower = NULL, ineqFun.upper = NULL, 
    control = list())

`par`	parameter vector(vector object).
`fun`	the objective function to be minimized. Currently, `fn` must take only one argument, and the parameter vector(`par`) will be passed to `fn` during the optimization. The first element of return value must be the evaluated value.
`par.lower, par.upper`	upper and lower bounds for parameter vector, respectively. Their length must equal to `length(par)`.
`eqA, ineqA`	the matrix objects that represents linear constraints. Its columns must be equal to `length(par)`, and its rows must be equal to the number of linear constraints.
`eqA.bound`	equality bounds for linear constraints, respectively. Their length must equal to the number of linear constraints.
`ineqA.lower, ineqA.upper`	upper and lower bounds for linear constraints, respectively. Their length must equal to the number of linear constraints.
`eqFun`	list object whose elements are functions that represents nonlinear equality constraints.
`eqFun.bound`	equality bounds for nonlinear constraints, respectively.
`ineqFun`	list object whose elements are functions that represents nonlinear lower and upper constraints.
`ineqFun.lower, ineqFun.upper`	lower and upper bounds for nonlinear constraints, respectively.
`control`	list of control parameters that define the behaviour of the solver. See `solnp2Control` for details.

An alternative interface which may be suited better for portfolio optimization compared with the default interface function solnp2.

A list with following elements:

`opt`	a list of information on the optimal solution as returned by the function `nlmin`.
`par`	a numeric vector, the optimal solution.
`objective`	a numeric value, the value at the optimal solution
`convergence`	an integer code. 0 indicates successful convergence.
`message`	a character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation.

The R port of dnonlp2 was written by Ryuichi Tamura, the R/Rmetrics interface solnp2NLP was written by Diethem Wuertz, the underlying C code called by the R function solnp2 was written by Peter Sperucci.

The PORT documentation is at http://netlib.bell-labs.com/cm/cs/cstr/153.pdf.

nlminb, nlminb2, nlminb2Control, and packages Rdonlp2 and Rsolnp2.

## Example:

   # Feasible Start Solution:
   start = c(10, 10)
   
   # Objective Function: x^2 + y^2 
   fun <- function(x) sum(x^2)
   
   # Bounds: -100 <= x,y <= 100
   par.lower = c(-100, -100)
   par.upper = c(100, 100)
    
   # Equality Constraints: x*y = 2
   eqFun <- list(
     function(x) x[1]*x[2])
   eqFun.bound = 2
  
   # Solution: x = c(sqrt(2), sqrt(2)), f(x) = 4   
   solnp2NLP(par = start, fun = fun, 
     par.lower = par.lower, par.upper = par.upper,
     eqFun = eqFun, eqFun.bound = eqFun.bound)[-1]