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Applications of Continuous Nonlinear Optimization

In: Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology

Author

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  • Neculai Andrei

    (Center for Advanced Modeling & Optimization
    Academy of Romanian Scientists)

Abstract

A number of 18 real continuous nonlinear optimization applications are presented in this chapter. These are used for numerical experiments and comparisons among the algorithms described in this book. For each application, the mathematical model, its GAMS representation, and the solution are given. GAMS is a standard technology for modeling and solving large-scale linear and nonlinear optimization applications. It is characterized by a very powerful language and a large number of different advanced optimization algorithms which are imbedded in this technology. The syntax of the GAMS language is not too complicated and practically all types of difficult nonlinear optimization applications can be represented and solved. Additionally, the nonlinear optimal control application, by discretization, can also be represented and solved by GAMS. Therefore, in this chapter, we include both continuous nonlinear optimization applications and some optimal control problems from different areas of activity. Some applications are from mechanical, electrical, and chemical engineering, heat transfer and fluid dynamics, and economic development. Others are from optimal control. The purpose is to present these applications in algebraic form and to see how all these can be represented and solved in GAMS. The solutions of these applications are determined by the optimization algorithms imbedded in the GAMS technology (MINOS, CONOPT, KNITRO, SNOPT, IPOPT) as well as some other packages described in this book (SPENBAR, DONLP, NLPQLP, filterSD) not imbedded in GAMS.

Suggested Citation

  • Neculai Andrei, 2017. "Applications of Continuous Nonlinear Optimization," Springer Optimization and Its Applications, in: Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology, chapter 0, pages 47-117, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-58356-3_4
    DOI: 10.1007/978-3-319-58356-3_4
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    Cited by:

    1. Qiwei Yang & Yantai Huang & Qiangqiang Zhang & Jinjiang Zhang, 2023. "A Bi-Level Optimization and Scheduling Strategy for Charging Stations Considering Battery Degradation," Energies, MDPI, vol. 16(13), pages 1-15, June.
    2. Neculai Andrei, 2018. "A Double-Parameter Scaling Broyden–Fletcher–Goldfarb–Shanno Method Based on Minimizing the Measure Function of Byrd and Nocedal for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 191-218, July.
    3. Martin Ćalasan & Tatjana Konjić & Katarina Kecojević & Lazar Nikitović, 2020. "Optimal Allocation of Static Var Compensators in Electric Power Systems," Energies, MDPI, vol. 13(12), pages 1-24, June.
    4. Neculai Andrei, 2020. "Diagonal Approximation of the Hessian by Finite Differences for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 859-879, June.

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