Package snobfit :: Module minq

Module minq

source code


Minimizes an affine quadratic form subject to simple bounds,
using coordinate searches and reduced subspace minimizations
using LDL^T factorization updates
    min    fval = gamma + c^T x + 0.5 x^T G x }
    s.t.   x in [xu,xo]

where G is a symmetric (n x n) matrix, not necessarily definite
(if G is indefinite, only a local minimum is found)

If G is sparse, it is assumed that the ordering is such that
a sparse modified Cholesky factorization is feasible

Usage:
------
[x,fval] = minq( gamma, c, G, xu, xo, prt, xx)

History:
--------
1) Ziwen Fu. 10/22/2008
   Directly Translate from minq.m ( v2.1 )

2) Ziwen Fu. 10/25/2008
   Python Class version of Minq

Classes
  Minq
Minimizes an affine quadratic form subject to simple bounds, using coordinate searches and reduced subspace minimizations using LDL^T factorization updates min fval = gamma + c^T x + 0.5 x^T G x } s.t.
Functions
 
minq(c, G, xlow, xhigh, x0=None, gamma=0, prt=0)
Minimizes an affine quadratic form subject to simple bounds, using coordinate searches and reduced subspace minimizations using LDL^T factorization updates min fval = gamma + c^T x + 0.5 x^T G x } s.t.
source code
Variables
  eps = 2.2204460492503131e-16
  inf = inf
Function Details

minq(c, G, xlow, xhigh, x0=None, gamma=0, prt=0)

source code 

Minimizes an affine quadratic form subject to simple bounds,
using coordinate searches and reduced subspace minimizations
using LDL^T factorization updates
     min    fval = gamma + c^T x + 0.5 x^T G x }
     s.t.   x in [xu,xo]

Inputs:
-------
c      a colomn vector.
G      a symmetric (n x n) matrix.
xlow   lower bound
xhigh  upper bound

Optional Inputs:
----------------
gamma  a constant.
prt    print level.
x0     initial guess.

Output:
-------
x      minimizer (but unbounded direction if info=1)
info   0  (local minimizer found)
       1  (unbounded below)
       99 (maxit exceeded)