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sqp: What are the equality and inequality constraint functions?

From: Sebastian Schubert
Subject: sqp: What are the equality and inequality constraint functions?
Date: Wed, 12 Jan 2011 17:45:50 +0100
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I have a non-linear, non-quadratic function to minimize with some 
constraints and sqp might be usable. However, I don't fully understand 
the manual. From the first part, especially,

Function File: [X, OBJ, INFO, ITER, NF, LAMBDA] = sqp (X, PHI, G,
     Solve the nonlinear program

               min phi (x)

     subject to

               g(x)  = 0
               h(x) >= 0
               lb <= x <= ub

it looks like there is only a constraint for every single element of x 
seperately (lb(1)<=x(1)<=ub(1), lb(2)<=x(2)<=ub(2), lb(3)<=x(3)<=ub(3), 
...). One of my constraints is 0 <= x(i) <= 1 so I do need this. In 
addition, I also need sum(x) = 1. With qp I was able to implement this 
but is this also possible with sqp? The manual speaks of "the equality 
and inequality constraint functions (which) must be of the form
  r = f (x)
in which X is a vector and R is a vector." How is this connected to the 
first part of the doc cited above?

Thank you

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