This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presen...
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This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinearprogramming. Our results demonstrate that constrained nonlinear programming is a worthwhile exercise for GARCH models, especially for the bivariate and trivariate cases, as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal VECH and the BEKK representations of the multivariate GARCH model.
TiO2 thin films were deposited on glass substrates by sputtering in a conventional rf magnetron sputtering system. X-ray diffraction pattern and transmission spectrum were measured. The curves of refraction index and ...
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TiO2 thin films were deposited on glass substrates by sputtering in a conventional rf magnetron sputtering system. X-ray diffraction pattern and transmission spectrum were measured. The curves of refraction index and extinction coefficient distributions as well as the thickness of films calculated from transmission spectrum were obtained. The optimization problem was also solved using a method based on a constrained nonlinear programming algorithm.
In this paper, a novel dynamical trajectory-based methodology is developed for systematically computing multiple local optimal solutions of general nonlinearprogramming problems with disconnected feasible components ...
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In this paper, a novel dynamical trajectory-based methodology is developed for systematically computing multiple local optimal solutions of general nonlinearprogramming problems with disconnected feasible components satisfying nonlinear equality/inequality constraints. The proposed methodology, deterministic in nature, exploits trajectories of two different non-linear dynamical systems to find multiple local optimal solutions. The methodology consists of two phases: Phase I starts from an arbitrary (infeasible) initial point and rinds systematically multiple or all the disconnected feasible components;Phase II finds an adjacent local optimal solution from a local optimum via a decomposition point, thereby systematically locating multiple local optimal solutions which lie within each feasible component found in Phase I. By alternating between these two phases, the methodology locates multiple or all the local optimal solutions which lie in all the disconnected feasible components. A theoretical foundation for the proposed methodology is also developed. The methodology is illustrated with a numerical example with promising results.
We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial vari...
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We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
In an accelerated degradation test, higher-than-normal stress levels are employed to hasten the degradation of product performance, and then the observed degradation data are used to estimate various reliability-relat...
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In an accelerated degradation test, higher-than-normal stress levels are employed to hasten the degradation of product performance, and then the observed degradation data are used to estimate various reliability-related quantities at the use (normal) condition. In this paper, optimal accelerated degradation test plans are developed under the assumptions of destructive testing and the simple constant rate relationship between the stress and the product performance. Specifically, the paper determines the stress levels, the proportion of test units allocated to each stress level, and the measurement times such that the asymptotic variance of the maximum likelihood estimator of the mean lifetime at the use condition is minimized. The optimization problem is formulated as a constrainednonlinear program, and exact optimal solutions are obtained for various cases. Sensitivity analysis and sample size determination procedures are also illustrated with an example.
The paper deals with two-person static Stackelberg games with quadratic objectives and common linear constraints for the leader and the follower. Important properties of the rational reaction function of the follower ...
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The paper deals with two-person static Stackelberg games with quadratic objectives and common linear constraints for the leader and the follower. Important properties of the rational reaction function of the follower could be derived from the outlined relations to the theory of parametric optimization. In the result the solution of the specified Stackelberg problem is reduced to the sequential solution of a finite number of standard constrained quadratic programming problems and the iterative selection of solution structures for the follower reaction. The implementation of the proposed algorithm stands on a large-scale nonlinearprogramming solver.
The increasing importance of nonlinearprogramming software requires an enlarged set of test examples. The purpose of this note is to point out how an interested mathematical programmer could obtain computer programs ...
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