The following is a list of some of the messages that can be returned in the "Procedure" column of the iterative output of an Optimization Toolbox function, along with a brief description of what they mean.
FMINCON and FSEMINF
Overly constrained -- The statement "Overly constrained" in the "Procedure" column means that the constraints used in the quadratic programming subproblem that the QPSUB function solves as part of the iteration for your Optimization Toolbox function are too strict. The quadratic programming solver is unable to find a point where the constraints are satisfied, but it can find one where the constraints are only violated by a very small amount (between 1e-8 and EPS.)
Therefore QPSUB is unable to state definitively that the subproblem is feasible, (it violates the constraints) but it is also unable to definitively state that the subproblem is infeasible. Roundoff error could be responsible for the constraint violation.
Hessian modified -- FMINCON had to modify the approximate Hessian matrix using small adjustments to the vectors used to update it during the construction of the quadratic programming subproblem in order to keep it positive definite. The assumption that the Hessian is positive definite is used to compute the steps necesary to solve the QP subproblem.
Hessian modified twice -- When this message is displayed, the approach FMINCON used for modifying the Hessian as described in "Hessian modified" was not sufficient to maintain a positive definite Hessian. Therefore it was forced to perturb the update vectors more than it did in the "Hessian modified" step in an attempt to preserve the positive definite Hessian.
Infeasible -- This indicates that the subproblem FMINCON has to solve is infeasible. This is a sign of high nonlinearity in the problem and indicates that your problem may take longer than normal to converge.
No update -- FMINCON returns this message when it detects that the problem may have been set up incorrectly or the function you are attempting to minimize is discontinuous.
FMINSEARCH:
initial -- This is the initial step FMINSEARCH uses to construct the simplex it will use in later steps to search for the answer.
expand -- The simplex FMINSEARCH uses to search for the answer has grown; FMINSEARCH has decided that it needs to examine a larger section of the feasible region to pinpoint the answer.
reflect -- The "reflect" option is very similar to the "shrink" option; however, "reflect" leaves most of the points alone and only replaces one with its reflection in the plane/hyperlane formed from its neighbors.
shrink -- The simplex FMINSEARCH uses to search for the answer has shrunk; FMINSEARCH has decided that it needs to focus on a larger section of the feasible region to pinpoint the answer.
contract inside -- FMINSEARCH needs to test another point; it tests a point part of the way between the last point it tested and the centroid of the other points that make up the simplex.
contract outside -- This is a combination of the reflect and contract inside options; FMINSEARCH reflects the last point tested around the centroid of the simplex, then chooses a point between that reflection and the centroid for its next test point.
FZERO:
initial -- FZERO is perfoming its initialization calculations.
search -- FZERO is searching for an interval containg a zero.
bisection -- FZERO is searching the interval for the zero using bisection.
interpolation -- FZERO is interpolating the data points already gathered to search for the zero.
FMINBND:
initial -- FMINBND is performing its initialization calculations.
golden -- FMINBND performs a golden section search.
parabolic -- FMINBND performs parabolic interpolation.
