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Simultaneous solution of linear equations and inequalities in max-algebra

Abdulhadi Aminu (2011)

Kybernetika

Let a ø p l u s b = max ( a , b ) and a ø t i m e s b = a + b for a , b ∈ ℝ . Max-algebra is an analogue of linear algebra developed on the pair of operations ( ø p l u s , ø t i m e s ) extended to matrices and vectors. The system of equations A ø t i m e s x = b and inequalities C ø t i m e s x ł e q d have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities.

Support properties of a family of connected compact sets

Josef Nedoma (2001)

Mathematica Bohemica

A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. A special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.

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