Importance/Applications of Optimization

• Importance

  Optimization provides an elegant blend of theory and applications. The theory uses elements beginning with elementary calculus and basic linear algebra and continues with functional and convex analysis. Applications of optimization involve science, engineering, economics, and industry. The wide and growing use of optimization make it essential for students and practitioners in every branch of science and technology.

• Applications (Examples)

  • Engineering

    • Find the equilibrium composition of a mixture of different atoms (GAMS Model at NEOS, using nonlinear programming and the KNITRO solver)
    • A Robotics path planning problem (AMPL Model at NEOS, using nonlinear semi-infinite programming and the NSIPS solver)

  • Scheduling/Optimal Allocation of Resources

    • Allocate aircrafts to routes (GAMS Model at NEOS, using linear programming and the BDMLP solver)
    • Find an optimal diet (AMPL model at NEOS using linear programming and the MOSEK solver) )
    • Egyptian Fertilizer Industry/Optimal Shipping Strategy (GAMS model at NEOS using linear programming and the MOSEK solver)

  • Mathematical Biology

    • Protein Folding at Princeton ( minimizing energy)

  • Information Theory

  • Financial Optimization

    • Risk management (GAMS Model at NEOS, using nonlinear programming and the KNITRO solver)
    • Markowitz model (AMPL Model at NEOS, using nonlinear programming and the LANCELOT solver) )

• NEOS Server Stories

• Suggested Texts/References:

  • Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

    by Aharon Ben-Tal and Arkadi Nemirovski
    MPS/SIAM Series on Optimization 2
    URL: http://www.ec-securehost.com/SIAM/MP02.html

  • Numerical Optimization

    Jorge Nocedal Stephen J. Wright
    URL: http://www.ece.northwestern.edu/~nocedal/book/num-opt.html

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