sqlp {sdpt3r}

Semidefinite Quadratic Linear Programming Solver

Description

sqlp solves a semidefinite quadratic linear programming problem using the SDPT3 algorithm of Toh et. al. (1999) returning both the primal solution X and dual solution Z.

Usage

sqlp(blk = NULL, At = NULL, C = NULL, b = NULL, control = NULL,
  X0 = NULL, y0 = NULL, Z0 = NULL)

Arguments

blk

A named-list object describing the block diagonal structure of the SQLP data

At

A list object containing constraint matrices for the primal-dual problem

C

A list object containing the constant $c$ matrices in the primal objective function

b

A vector containing the right hand side of the equality constraints in the primal problem

control

A list object specifying the values of certain parameters. If not provided, default values are used

X0

An initial iterate for the primal solution variable X. If not provided, an initial iterate is computed internally.

y0

An initial iterate for the dual solution variable y. If not provided, an initial iterate is computed internally.

Z0

An initial iterate for the dual solution variable Z. If not provided, an initial iterate is computed internally.

Details

A full mathematical description of the problem to be solved, details surrounding the input variables, and discussion regarding the output variables can be found in the accompanying vignette.

Value

X

A list containing the solution matrix to the primal problem

y

The solution vector to the dual problem

Z

A list containing the solution matrix to the dual problem

pobj

The achieved value of the primary objective function

dobj

The achieved value of the dual objective function

References

K.C. Toh, M.J. Todd, and R.H. Tutuncu, SDPT3 — a Matlab software package for semidefinite programming, Optimization Methods and Software, 11 (1999), pp. 545–581. R.H Tutuncu, K.C. Toh, and M.J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3, Mathematical Programming Ser. B, 95 (2003), pp. 189–217.

Examples

blk = c("l" = 2)
C = matrix(c(1,1),nrow=1)
A = matrix(c(1,3,4,-1), nrow=2)
At = t(A)
b = c(12,10)
out = sqlp(blk,list(At),list(C),b)