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A penalty approach to a discretized double obstacle problem with derivative constraints

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  • Song Wang

Abstract

This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating the mixed nonlinear complementarity problem representing the Karush–Kuhn–Tucker conditions of the optimization problem. We then show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the equation. Numerical experiments, carried out on a non-trivial test problem to verify the theoretical finding, show that the computed rates of convergence match the theoretical ones well. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Song Wang, 2015. "A penalty approach to a discretized double obstacle problem with derivative constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 775-790, August.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:775-790
    DOI: 10.1007/s10898-014-0262-3
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    References listed on IDEAS

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    1. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    2. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    3. R. D. C. Monteiro & Jong-Shi Pang, 1996. "Properties of an Interior-Point Mapping for Mixed Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 629-654, August.
    4. Damgaard, Anders, 2006. "Computation of reservation prices of options with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 415-444, March.
    5. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    6. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
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    Cited by:

    1. Yarui Duan & Song Wang & Yuying Zhou, 2021. "A power penalty approach to a mixed quasilinear elliptic complementarity problem," Journal of Global Optimization, Springer, vol. 81(4), pages 901-918, December.

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