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Geometric Programming

In: Mathematical Optimization and Economic Analysis

Author

Listed:
  • Mikuláš Luptáčik

    (WU Vienna University of Economics and Business, Department of Economics)

  • Klaus Prettner

    (WU Vienna University of Economics and Business, Department of Economics)

Abstract

This chapter explores geometric programming as a method suitable for widely used classes of nonlinear problems, especially in engineering and production economics. It describes optimization problems in which the functions in the constraints and the objective function are polynomials with positive coefficients (called posynomials) and their transformation into convex forms. After discussing duality in geometric programming with the focus on the economic interpretation, the chapter presents cost minimization under production constraints and a nonlinear input–output model with substitution between primary factors as illustrative examples. A particular focus here is on the effects of automation on employment in a multisectoral setting showing the potential and usefulness of the geometric programming duality for qualitative economic analysis.

Suggested Citation

  • Mikuláš Luptáčik & Klaus Prettner, 2026. "Geometric Programming," Springer Optimization and Its Applications, in: Mathematical Optimization and Economic Analysis, edition 0, chapter 6, pages 205-235, Springer.
    • Handle: RePEc:spr:spochp:978-1-0716-5076-9_6
    DOI: 10.1007/978-1-0716-5076-9_6
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