An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the FritzJohn necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the KarushKuhn-Tucker conditions.
In production, an intelligent analysis of the data provided along the production line bears huge potential for increasing process efficiency and reducing production costs. The (continuous) collection of relevant data is a crucial precondition for every Industry 4.0 or smart technology. While new machines have internal controllers and sensors to meet those requirements, this is usually not the case for machines being already in use. Especially in the textile industry, it is often standard to keep old machines since the manufacturing methods themselves haven't changed significantly over the past decades. Hence, the successful exploitation of digitalization advantages requires these companies to first develop and implement a digitization strategy. In this paper we present a concept which allows to develop modular, scalable, flexible solutions considering the whole digitization process from data acquisition to storage. The concept is complemented by a guideline for its application in industry. Experience from a prototypical application in a textile company is described. The concept enables companies to determine the various conditions and requirements for digitization, to analyze different possibilities and to deduce scenarios that lead to a solution for the effective utilization of Industry 4.0 technologies.
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