Abstract
The partially-linear models can be successfully applied in economics and technology, which increases the interest in them. Every continuous partially-linear function with a finite number of linear parts can be presented by means of linear functions and maximum of the functions. We considear graph interpretation of this optimization problem. Partially-linear problems are commonly not only nondifferentiable but nonconvex, which makes their solution by standard optimization methods difficult. In this work we give the necessary and sufficient conditions for local optimality. An algorithm for solving such problems, based on the constructive optimization methods is suggested
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