An improved dynamic contact model for mass-spring and finite element systems is proposed in this paper. The proposed model avoids the numerical troubles of spurious high-frequency oscillations for mass-spring and fini...
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An improved dynamic contact model for mass-spring and finite element systems is proposed in this paper. The proposed model avoids the numerical troubles of spurious high-frequency oscillations for mass-spring and finite element systems in dynamic contact problems by using the parametric quadratic programming technique. The iterative process for determination of contact states are not required for each time step in the proposed method, as the contact states are transformed into the base exchanges in the solution of a standard quadraticprogramming problem. The proposed methodology improves stability and has good convergence behavior for dynamic contact problems. Numerical results demonstrate the validity of the proposed method.
Aiming to simplify the solution process of elasto-plastic problems, this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto-plasticity. The parame...
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Aiming to simplify the solution process of elasto-plastic problems, this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto-plasticity. The parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto-plastic behaviour and can also be exploited for numerical iteration. Examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method. Copyright (C) 2002 John Wiley Sons, Ltd.
Despite the volume of research conducted on efficient frontiers, in many cases it is still not the easiest thing to compute a mean-variance (MV) efficient frontier even when all constraints are linear. This is particu...
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Despite the volume of research conducted on efficient frontiers, in many cases it is still not the easiest thing to compute a mean-variance (MV) efficient frontier even when all constraints are linear. This is particularly true of large-scale problems having dense covariance matrices and hence they are the focus in this paper. Because standard approaches for constructing an efficient frontier one point at a time tend to bog down on dense covariance matrix problems with many more than about 500 securities, we propose as an alternative a procedure of parametric quadratic programming for more effective usage on large-scale applications. With the proposed procedure we demonstrate through computational results on problems in the 1000-3000 security range that the efficient frontiers of dense covariance matrix problems in this range are now not only solvable, but can actually be computed in quite reasonable time. (C) 2009 Elsevier B.V. All rights reserved.
A method is presented for the solution of the parametric quadratic programming problem by the use of conjugate directions. It is based on the method for quadraticprogramming proposed by the author in [1].
A method is presented for the solution of the parametric quadratic programming problem by the use of conjugate directions. It is based on the method for quadraticprogramming proposed by the author in [1].
It is well known that the performance of a kernel method highly depends on the choice of kernel parameter. A kernel path provides a compact representation of all optimal solutions, which can be used to choose the opti...
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It is well known that the performance of a kernel method highly depends on the choice of kernel parameter. A kernel path provides a compact representation of all optimal solutions, which can be used to choose the optimal value of kernel parameter along with cross validation (CV) method. However, none of these existing kernel path algorithms provides a unified implementation to various learning problems. To fill this gap, in this paper, we first study a general parametric quadratic programming (PQP) problem that can be instantiated to an extensive number of learning problems. Then we provide a generalized kernel path (GKP) for the general PQP problem. Furthermore, we analyze the iteration complexity and computational complexity of GKP. Extensive experimental results on various benchmark datasets not only confirm the identity of GKP with several existing kernel path algorithms, but also show that our GKP is superior to the existing kernel path algorithms in terms of generalization and robustness. (c) 2021 Elsevier Ltd. All rights reserved.
A method is proposed for finding local minima to the parametric general quadraticprogramming problem where all the coefficients are linear or polynomial functions of a scalar parameter. The local minimum vector and t...
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A method is proposed for finding local minima to the parametric general quadraticprogramming problem where all the coefficients are linear or polynomial functions of a scalar parameter. The local minimum vector and the local minimum value are determined explicitly as rational functions of the parameter. A numerical example is given.
Many practical applications lead to optimization problems that can either be stated as quadraticprogramming (QP) problems or require the solution of QP problems on a lower algorithmic level. One relatively recent app...
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Many practical applications lead to optimization problems that can either be stated as quadraticprogramming (QP) problems or require the solution of QP problems on a lower algorithmic level. One relatively recent approach to solve QP problems are parametric active-set methods that are based on tracing the solution along a linear homotopy between a QP problem with known solution and the QP problem to be solved. This approach seems to make them particularly suited for applications where a-priori information can be used to speed-up the QP solution or where high solution accuracy is required. In this paper we describe the open-source C++ software package qpOASES, which implements a parametric active-setmethod in a reliable and efficient way. Numerical tests show that qpOASES can outperform other popular academic and commercial QP solvers on small-to medium-scale convex test examples of the Maros Meszaros QP collection. Moreover, various interfaces to third-party software packages make it easy to use, even on embedded computer hardware. Finally, we describe how qpOASES can be used to compute critical points of nonconvex QP problems.
作者：
Qi, YueNankai Univ
China Acad Corp Governance 94 Weijin Rd Tianjin 300071 Peoples R China Nankai Univ
Dept Financial Management Business Sch 94 Weijin Rd Tianjin 300071 Peoples R China Nankai Univ
Collaborat Innovat Ctr China Econ 94 Weijin Rd Tianjin 300071 Peoples R China
Portfolio selection is recognised as the birth-place of modern finance;portfolio optimisation has become a developed tool. However, efficient frontiers are piece-wisely made up by connected parabolic segments;such str...
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Portfolio selection is recognised as the birth-place of modern finance;portfolio optimisation has become a developed tool. However, efficient frontiers are piece-wisely made up by connected parabolic segments;such structure can be rendered only by parametric quadratic programming. Overlooking the structure can both get incomplete results and cause difficulties in e-constraint approaches or weighted-sums approaches. There has been no research to systematically parametrically compute efficient frontiers and report and analyse the structure up until now;in such an area, this article contributes to the literature. I utilise the software of parametric quadratic programming, set up practical portfolio selection models, build batches of 5-stock problems up to 1800-stock problems, analyse the structure, and report the findings. For example, the numbers of parabolic segments can quadratically increase with problem sizes, so fixed numbers of points are insufficient approximations of efficient frontiers. Contrary to common assumptions, an efficient frontier is not smooth in the presence of kinks. Moreover, I utilise the structure for rebalancing portfolios, propose two models to minimise rebalancing cost, transform them into linear programming or integer programming, and solve them. This article can help scholars and practitioners obtain a comprehensive picture of efficient frontiers and perceive the structure.
Boundary slippage modeling and optimization of the hydrophobic tilting pad thrust bearing with elastic deformation are conducted to obtain the optimal lubricating film geometry and power loss. The modified Reynolds eq...
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Boundary slippage modeling and optimization of the hydrophobic tilting pad thrust bearing with elastic deformation are conducted to obtain the optimal lubricating film geometry and power loss. The modified Reynolds equation combining with a nonlinear slip control equation of the limiting shear stress model is transformed to a series of linear complementary problems to be solved by the parametric quadratic programming technique. An optimization approach based on the Kriging surrogate model is developed to optimize the slip/no-slip configuration of the thrust pad. The effect of homogeneous slipping and heterogeneous slip/no-slipping coupled with elastic deformation on minimum film thickness and power loss is studied for the tilting pad thrust bearing with the flexible lining materials.
This paper deals with the efficient implementation of parametric quadratic programming that is specialized for large-scale mean-variance portfolio selection with a dense covariance matrix. The aim is to calculate the ...
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This paper deals with the efficient implementation of parametric quadratic programming that is specialized for large-scale mean-variance portfolio selection with a dense covariance matrix. The aim is to calculate the whole Pareto front of solutions that represent the trade-off between maximizing expected return and minimizing variance of return. We describe and compare in a uniform framework several techniques to speed up the necessary matrix operations, namely the initial matrix decomposition, the solution process in each iteration, and the matrix updates. Techniques considered include appropriate ordering of the matrix rows and columns, reducing the size of the system of linear equations, and dividing the system into two parts. Regarding implementation, we suggest to simultaneously use two different matrix representations that are specifically adapted to certain parts of the algorithm and propose a technique that prevents algorithm stalling due to numerical errors. Finally, we analyse and compare the runtime of these algorithm variants on a set of benchmark problems. As we demonstrate, the most sophisticated variant is several orders of magnitude faster than the standard implementation on all tested problem instances. (c) 2007 Elsevier Ltd. All rights reserved.
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