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Scalar and Vector Optimization with Composed Objective Functions and Constraints

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

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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.

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References

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany

    Nicole Lorenz

  2. Faculty of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany

    Gert Wanka

Authors
  1. Nicole Lorenz
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  2. Gert Wanka
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Corresponding author

Correspondence to Nicole Lorenz .

Editor information

Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Lorenz, N., Wanka, G. (2013). Scalar and Vector Optimization with Composed Objective Functions and Constraints. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_8

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