An enumerative method for convex programs with linear complementarity constraints and application to the bilevel problem of a forecast model for high complexity products
The increasing variety of high complexity products presents a challenge in acquiring
detailed demand forecasts. Against this backdrop, a convex quadratic
parameter dependent forecast model is revisited, which calculates a prognosis
for structural parts based on historical order data. The parameter dependency
inspires a bilevel problem with convex objective function, that allows for the calculation
of optimal parameter settings in the forecast model. The bilevel problem
can be formulated as a mathematical problem with equilibrium constraints
(MPEC), which has a convex objective function and linear constraints.
Several new enumerative methods are presented, that find stationary points or
global optima for this problem class. An algorithmic concept shows a recursive
pattern, which finds global optima of a convex objective function on a general
non-convex set defined by a union of polytopes. Inspired by these concepts the
thesis investigates two implementations for MPECs, a search algorithm and a
hybrid algorithm.
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