Lipschitz upper semicontinuity in linear optimization
J. Camacho Moro, M. J. Cánovas Cánovas, J. Parra López
This talk is focussed on computing the Lipschitz upper semicontinuity modulus of the argmin mapping for canonically perturbed linear programs. In contrast to the feasible set mapping, here we have to overcome the nonconvexity of the graph. This is done by introducing the weaker concept of local directional convexity, which is shown to be satisfied by the argmin mapping. With this tool, we succeed to provide a practically computable expression for the Lipschitz upper semicontinuity modulus as the máximum of finitely many calmness moduli. Despite the striking resemblance of this result with its counterpart for the feasible set mapping, the methodology followed for the argmin mapping is notably different.
Keywords: Lipschitz upper semicontinuity, calmness, argmin mapping, linear programming.
Scheduled
GT11 Continuous Optimization I
June 9, 2022 10:10 AM
A12
Other papers in the same session
M. López Cerdá
J. Castro, L. F. Escudero, J. F. Monge
M. Rodríguez Álvarez, J. Vicente-Pérez
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