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Scalar and Vector Optimization with Composed Objective Functions and Constraints

In: Optimization, Simulation, and Control

Author

Listed:
  • Nicole Lorenz

    (Chemnitz University of Technology)

  • Gert Wanka

    (Chemnitz University of Technology)

Abstract

In this chapter we consider scalar and vector optimization problems with objective functions being the composition of a convex function and a linear mapping and cone and geometric constraints. By means of duality theory we derive dual problems and formulate weak, strong, and converse duality theorems for the scalar and vector optimization problems with the help of some generalized interior point regularity conditions and consider optimality conditions for a certain scalar problem.

Suggested Citation

  • Nicole Lorenz & Gert Wanka, 2013. "Scalar and Vector Optimization with Composed Objective Functions and Constraints," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 107-130, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_8
    DOI: 10.1007/978-1-4614-5131-0_8
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