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An Improved Dynamic Contact Model for Mass-Spring and Finite Element Systems Based on parametric quadratic programming Method

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2018年第2期15卷 1-12页

作者： Zhu, Bao Li, Hongxia Dalian Univ Technol Sch Mat Sci & Engn Dalian Liaoning Peoples R China Dalian Univ Technol Sch Mech Engn Dalian Liaoning Peoples R China

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 quadratic programming problem. The proposed methodology improves stability and has good convergence behavior for dynamic contact problems. Numerical results demonstrate the validity of the proposed method.

关键词： Dynamic Contact Problem Finite Element Method Mass-Spring Model parametric quadratic programming Linear Complementarity

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Elasto-plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2002年第6期55卷 669-683页

作者： Liew, KM Wu, YC Zou, GP Ng, TY Nanyang Technol Univ Sch Mech & Prod Engn Natl Ctr Supercomp & Visualisat Singapore 639798 Singapore Inst High Performance Comp Singapore 118261 Singapore

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.

关键词： parametric quadratic programming elasto-plasticity reproducing kernel particle method (RKPM)

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Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期204卷 581-588页

作者： Hirschberger, Markus Qi, Yue Steuer, Ralph E. Univ Georgia Dept Banking & Finance Athens GA 30602 USA Univ Eichstatt Ingolstadt Dept Math Eichstatt Germany Nankai Univ Coll Business Dept Financial Management Tianjin 300071 Peoples R China

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.

关键词： Bi-criterion Portfolio selection parametric quadratic programming Efficient frontiers Dense covariance matrices Large-scale Hyperbolic segments

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ONE WAY TO SOLVE THE parametric quadratic-programming PROBLEM

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MATHEMATICAL programming 1981年第2期21卷 224-228页

作者： BENVENISTE, R University of Birmingham P.O. Box 363 Birmingham United Kingdom

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 quadratic programming proposed by the author in [1].

关键词： parametric quadratic programming Reduced Problem Reduced Gradient Conjugate Direction

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A kernel path algorithm for general parametric quadratic programming problem

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PATTERN RECOGNITION 2021年 116卷 107941-107941页

作者： Gu, Bin Xiong, Ziran Yu, Shuyang Zheng, Guansheng Nanjing Univ Informat Sci & Technol Sch Comp & Software Nanjing Peoples R China Mohamed Bin Zayed Univ Artificial Intelligence Abu Dhabi U Arab Emirates Northeastern Univ Sch Comp Sci & Engn Shenyang Peoples R China

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.

关键词： Kernel path QR decomposition parametric quadratic programming Cross validation

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A UNIFIED APPROACH TO ONE-parametric GENERAL quadratic-programming

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MATHEMATICAL programming 1985年第3期33卷 318-338页

作者： VALIAHO, H 1.Department of Mathematics University of Helsinki Helsinki Finland

A method is proposed for finding local minima to the parametric general quadratic programming 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.

关键词： General quadratic programming parametric quadratic programming Pivotal Operation Principal Pivoting quadratic Forms Subject to Linear Constraints

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qpOASES: a parametric active-set algorithm for quadratic programming

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MATHEMATICAL programming COMPUTATION 2014年第4期6卷 327-363页

作者： Ferreau, Hans Joachim Kirches, Christian Potschka, Andreas Bock, Hans Georg Diehl, Moritz ABB Corp Res Segelhofstr 1K CH-5405 Baden Switzerland Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR D-69120 Heidelberg Germany Katholieke Univ Leuven ESAT STADIUS OPTEC Eletr Engn Dept B-3001 Leuven Belgium Univ Freiburg IMTEK Dept Microsyst Engn D-79110 Freiburg Germany

Many practical applications lead to optimization problems that can either be stated as quadratic programming (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.

关键词： parametric quadratic programming Active set method Model predictive control

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parametrically computing efficient frontiers of portfolio selection and reporting and utilizing the piecewise-segment structure

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2020年第10期71卷 1675-1690页

作者： Qi, Yue Nankai 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 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.

关键词： Multi-objective quadratic programming parametric quadratic programming portfolio selection efficient set nondominated set

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Boundary slippage modeling and optimization of hydrophobic tilting pad thrust bearing with elastic deformation

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TRIBOLOGY INTERNATIONAL 2019年 136卷 299-316页

作者： Zhu, B. Li, Y. P. Wang, W. G. Lei, M. K. Dalian Univ Technol Surface Engn Lab Sch Mat Sci & Engn Dalian 116024 Peoples R China

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.

关键词： Tilting pad thrust bearing Elastohydrodynamic lubrication Boundary slippage parametric quadratic programming Kriging surrogate model

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Efficient implementation of an active set algorithm for large-scale portfolio selection

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COMPUTERS & OPERATIONS RESEARCH 2008年第12期35卷 3945-3961页

作者： Stein, Michael Branke, Juergen Schmeck, Hartmut Univ Karlsruhe TH Inst Appl Informat & Formal Descript Methods Karlsruhe Germany

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.

关键词： parametric quadratic programming mean-variance portfolio selection dense covariance matrix efficient implementation

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