Re: Behaviour of FMINCON - question.
- From: "pluton" <plutonesque@xxxxxxxxx>
- Date: 28 Mar 2006 07:46:31 -0800
Maybe you can try to get some of the references mentionned above.
Matlab Help browser :
Algorithm
Large-Scale Optimization
The large-scale algorithm is a subspace trust region method and is
based on the interior-reflective Newton method described in [1], [2].
Each iteration involves the approximate solution of a large linear
system using the method of preconditioned conjugate gradients (PCG).
See the trust region and preconditioned conjugate gradient method
descriptions in the Large-Scale Algorithms chapter.
Medium-Scale Optimization
fmincon uses a sequential quadratic programming (SQP) method. In this
method, the function solves a quadratic programming (QP) subproblem at
each iteration. An estimate of the Hessian of the Lagrangian is updated
at each iteration using the BFGS formula (see fminunc, references [7],
[8]).
A line search is performed using a merit function similar to that
proposed by [4], [5], and [6]. The QP subproblem is solved using an
active set strategy similar to that described in [3]. A full
description of this algorithm is found in Constrained Optimization in
Standard Algorithms.
See also SQP Implementation in Standard Algorithms for more details on
the algorithm used.
Limitations
fmincon only handles real variables.
The function to be minimized and the constraints must both be
continuous. fmincon might only give local solutions.
When the problem is infeasible, fmincon attempts to minimize the
maximum constraint value.
The objective function and constraint function must be real-valued;
that is, they cannot return complex values.
The large-scale method does not allow equal upper and lower bounds. For
example if lb(2)==ub(2), then fmincon gives the error
Equal upper and lower bounds not permitted in this large-scale
method.
Use equality constraints and the medium-scale method instead.
If you only have equality constraints you can still use the large-scale
method. But if you have both equalities and bounds, you must use the
medium-scale method.
See Also
@ (function_handle), fminbnd, fminsearch, fminunc, optimset
References
[1] Coleman, T.F. and Y. Li, "An Interior, Trust Region Approach for
Nonlinear Minimization Subject to Bounds," SIAM Journal on
Optimization, Vol. 6, pp. 418-445, 1996.
[2] Coleman, T.F. and Y. Li, "On the Convergence of Reflective Newton
Methods for Large-Scale Nonlinear Minimization Subject to Bounds,"
Mathematical Programming, Vol. 67, Number 2, pp. 189-224, 1994.
[3] Gill, P.E., W. Murray, and M.H. Wright, Practical Optimization,
London, Academic Press, 1981.
[4] Han, S.P., "A Globally Convergent Method for Nonlinear
Programming," Vol. 22, Journal of Optimization Theory and Applications,
p. 297, 1977.
[5] Powell, M.J.D., "A Fast Algorithm for Nonlinearly Constrained
Optimization Calculations," Numerical Analysis, ed. G.A. Watson,
Lecture Notes in Mathematics, Springer Verlag, Vol. 630, 1978.
[6] Powell, M.J.D., "The Convergence of Variable Metric Methods For
Nonlinearly Constrained Optimization Calculations," Nonlinear
Programming 3 (O.L. Mangasarian, R.R. Meyer, and S.M. Robinson, eds.),
Academic Press, 1978.
.
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