LINCOA

LINCOA (LINearly Constrained Optimization Algorithm) is a numerical optimization algorithm by Michael J. D. Powell. It is also the name of Powell's Fortran 77 implementation of the algorithm.

LINCOA solves linearly constrained optimization problems without using derivatives of the objective function, which makes it a derivative-free algorithm. The algorithm solves the problem using a trust region method that forms quadratic models by interpolation. One new point is computed on each iteration, usually by solving a trust region subproblem subject to the linear constraints, or alternatively, by choosing a point to replace an interpolation point that may be too far away for reliability. In the second case, the new point may not satisfy the linear constraints.

The same as NEWUOA, LINCOA constructs the quadratic models by the least Frobenius norm updating technique. A model function is determined by interpolating the objective function at ${\displaystyle m}$ (an integer between ${\displaystyle n+2}$ and ${\displaystyle (n+1)(n+2)/2}$) points; the remaining freedom, if any, is taken up by minimizing the Frobenius norm of the change to the model's Hessian (with respect to the last iteration).

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