662 research outputs found

    Optimal control of multiphase steel production

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    An optimal control problem for the production of multiphase steel is investigated, where the state equations are a semilinear heat equation and an ordinary differential equation, which describes the evolution of the ferrite phase fraction. The optimal control problem is analyzed and the first-order necessary and second-order sufficient optimality conditions are derived. For the numerical solution of the control problem reduced sequential quadratic programming (rSQP) method with a primal-dual active set strategy (PDAS) was applied. The numerical results were presented for the optimal control of a cooling line for production of hot rolled Mo-Mn dual phase steel

    Fast iterative solution of reaction-diffusion control problems arising from chemical processes

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    PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

    Optimal control of multiphase steel production

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    An optimal control problem for the production of multiphase steel is investigated that takes into account phase transformations in the steel slab. The state equations are a semilinear heat equation coupled with an ordinary differential equation, that describes the evolution of the steel microstructure. The time-dependent heat transfer coefficient serves as a control function. Necessary and sufficient optimality conditions for the control problem are derived. For the numerical solution of the control problem, a reduced sequential quadratic programming method with a primal-dual active set strategy is developed. The numerical results are presented for the optimal control of a cooling line in the production of hot-rolled Mo–Mn dual phase steel. © 2019, The Author(s)

    A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

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    Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.Dupire equation, parameter identification, optimal control, optimality conditions, SQP method, primal-dual active set strategy

    SUFFICIENT OPTIMALITY CONDITIONS FOR THE MOREAU-YOSIDA TYPE REGULARIZATION CONCEPT APPLIED TO SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE STATE CONSTRAINTS

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    We develop sufficient optimality conditions for a Moreau-Yosidaregularized optimal control problem governed by a semilinear ellipticPDE with pointwise constraints on the state and the control. We makeuse of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept,for which standard second order sufficient conditions have been shown. Moreover, we present a numerical example,solving a Moreau-Yosida regularized model problem with an SQP method

    Rotor design optimization using a free wake analysis

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    The aim of this effort was to develop a comprehensive performance optimization capability for tiltrotor and helicopter blades. The analysis incorporates the validated EHPIC (Evaluation of Hover Performance using Influence Coefficients) model of helicopter rotor aerodynamics within a general linear/quadratic programming algorithm that allows optimization using a variety of objective functions involving the performance. The resulting computer code, EHPIC/HERO (HElicopter Rotor Optimization), improves upon several features of the previous EHPIC performance model and allows optimization utilizing a wide spectrum of design variables, including twist, chord, anhedral, and sweep. The new analysis supports optimization of a variety of objective functions, including weighted measures of rotor thrust, power, and propulsive efficiency. The fundamental strength of the approach is that an efficient search for improved versions of the baseline design can be carried out while retaining the demonstrated accuracy inherent in the EHPIC free wake/vortex lattice performance analysis. Sample problems are described that demonstrate the success of this approach for several representative rotor configurations in hover and axial flight. Features that were introduced to convert earlier demonstration versions of this analysis into a generally applicable tool for researchers and designers is also discussed
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