next up previous contents index
Next: Solver Performance and Statistics Up: DSDP with MATLAB Previous: LP Cones   Contents   Index

Solver Options

There are more ways to call the solver. The command

> [STAT,y,X] = DSDP(b,AC,OPTIONS)
specifies some options for the solver. The OPTIONS structure may contain any of the following fields that may significantly affect the performance of the solver. Options that affect the formulation of the problem are:
l
[r0 ] is the multiple of the identity matrix added to the initial variable $S$ in (DD). Specifically, $S^0 = C- \sum A_iy_i^0 + r^0*I$. If $r0<0$, a dynamic selection will be used that selects a very large number ( 1e10). IMPORTANT: To improve convergence, use a smaller value. [default -1 (Heuristic)].
l
[zbar] an upper bound $\bar{z}$ on the objective value at the solution [default 1.0e10].
l
[penalty] penalty parameter $\Gamma$ in (DD) that enforces feasibility in (D). IMPORTANT: This parameter must be positive and greater than the trace of the solution $X$ of (P). [default 1e8].
l
[boundy] determines the bounds $l$ and $u$ on the variables $y$ in (DD). That is, $-boundy = l \leq y_i \leq u = boundy$ for all $i=1, \ldots, m$. The convergence of this solver assumes the solution set of these variables is bounded. These bounds do not have to be tight. The default value is 1e6, but smaller bounds may improve performance.
Fields in the OPTIONS structure that affect the stopping criteria for the solver are:
l
[gaptol] tolerance for duality gap as a fraction of the value of the objective functions [default 1e-6].
l
[maxit] maximum number of iterations allowed [default 1000].
l
[steptol] tolerance for stopping because of small steps [default 1e-2].
l
[inftol] the value $r$ in (DD) must be less than this tolerance to classify the final solution of (D) as feasible. [default 1e-8].
l
[dual_bound] an upper bound for the objective value in (D). The solver stops when it finds a feasible point of (D) with an objective greater than this value. (Helpful in branch-and-bound algorithms.) [default 1e+30].

Fields in the OPTIONS structure that affect printing are:
l
[print] = k to display output in each k iteration, else = 0 [default 10]. (See Section: 3 to interpret the output).
l
[logtime] =1 to profile the performance of DSDP subroutines, else =0. (Assumes proper compilation flags.)
l
[cc] add this constant the objective value. This parameter is algorithmically irrelevant, but it can make the objective values displayed on the screen more consistent with the underlying application [default 0].

Other fields recognized in OPTIONS structure are:
l
[rho] to set the potential parameter $\rho$ in the function (1) to this multiple of the conic dimension $n$. [default: 3] IMPORTANT! Increasing this parameter to 4 or 5 may significantly improve performance.
l
[dynamicrho] to use dynamic rho strategy. [default: 1].
l
[bigM] if $ > 0$, the variable $r$ in (DD) will remain positive (as opposed to nonegative). [default 0].
l
[mu0 ] initial barrier parameter. $\mu= (\bar z - b^T y^k )/(\rho)$. [default -1: use heuristic]
l
[reuse] sets a maximum on the number of times the Schur complement matrix can be reused. Larger numbers reduce the number of iterations but increase the cost of each iteration. Applications requiring few iterations (<60) should consider setting this parameter to 0. [default: 4]

For instance, the commands

> OPTIONS.gaptol = 0.001;
> OPTIONS.boundy = 1000;
> OPTIONS.rho = 5;
> [STAT,y,X] = DSDP(b,AC,OPTIONS);
asks for a solution with approximately three significant digits, bound the $y$ variables by $-1000 $ and $+1000$, and use a potential parameter $\rho$ of 5 times the conic dimension. Some of these fields, especially rho, r0, and ybound can significantly improve performance of the solver.

Using a fourth input argument, the command

> [STAT,y,X] = DSDP(b,AC,OPTIONS,y0);
specifies an initial solution y0 in (D). The default starting vector is the zero vector.


next up previous contents index
Next: Solver Performance and Statistics Up: DSDP with MATLAB Previous: LP Cones   Contents   Index
Steven Benson 2005-02-11