Methods of Optimization and Optimal Control in Plane Geometry
Anita Kripfganz
A special kind of geometrical problems is concerned with
extremal charakteristic parameters of plane convex figures. The considered
figures are characterized by some other fixed charakteristic parameters. Such a
type of problems can be formulated as constrained extremal problem in the space
of convex figures. Some of them are successfully investigated by use of
optimization methods and methods of optimal control like duality theory or
Pontrjagin's Maximum Principle.
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Solution Branching in Partition Problems
Anita Kripfganz
We consider partitioning (allocation) problems with
nonlinear total cost function and a linking constraint for the resource. Single
projects are rated with the same convex-concave cost function, the total costs
are additively composed. The structure of the optimal solution is to be find in
dependence on the linking parameter. Under some additional conditions for the
convex-concave partial cost function one can observe a branching behavior
between symmetric and certain non-symmetric partitions.
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