A Trust Region SQP Algorithm for Mixed-Integer Nonlinear Programming
O. Exler,
K. Schittkowski: Optimization Letters, Vol. 1, 269-280 (2007)
Abstract:
We propose a modified sequential quadratic programming (SQP) method for solving
mixed-integer nonlinear programming problems. Under the assumption that integer
variables have a 'smooth' influence on the model functions, i.e., that function
values do not change drastically when in- or decrementing an integer value,
successive quadratic approximations are applied. The algorithm is stabilized by
a trust region method with Yuan's second order corrections. It is not assumed
that the mixed-integer program is relaxable. In other words, function values can
be evaluated only at integer points. The Hessian of the Lagrangian function is
approximated by BFGS updates subject to the continuous and diagonal second order
information subject to the integer variables. Numerical results are presented
for a set of 80 mixed integer test problems taken from the literature.
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