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A cutting plane algorithm for MV portfolio selection model

APPLIED MATHEMATICS AND COMPUTATION 2009年第4期215卷 1456-1462页

作者： Chen, Guohua Liao, Xiaolian Wang, Shouyang Hunan Inst Humanities Sci & Technol Dept Math Loudi 417000 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Syst Sci Beijing 100080 Peoples R China

This paper deals with a portfolio selection problem with fuzzy return rates. A possibilistic mean variance (FMVC) portfolio selection model was proposed. The possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory. For such problems there are no special standard algorithms. We propose a cutting plane algorithm to solve (FMVC). The nonlinear programming problem can be solved by sequence linear programming problem. A numerical example is given to illustrate the behavior of the proposed model and algorithm. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Possibility theory Portfolio selection cutting plane algorithm

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Multiple kernel multivariate performance learning using cutting plane algorithm

Multiple kernel multivariate performance learning using cutt...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Wang, Jingbin Wang, Haoxiang Zhou, Yihua McDonald, Nancy Chinese Acad Sci Natl Time Serv Ctr Xian 710600 Peoples R China Chinese Acad Sci Grad Univ Beijing 100039 Peoples R China Cornell Univ Dept Elect & Comp Engn Ithaca NY 14850 USA Lehigh Univ Dept Mech Engn & Mech Bethlehem PA 18015 USA Tulane Univ Dept Comp Sci New Orleans LA 70118 USA

ISBN: (纸本)9781479986965

In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel parameter tuning, we proposed to construct an optimal kernel by weighted linear combination of some candidate kernels. The learning of the classifier parameter and the kernel weight are unified in a single objective function considering to minimize the upper boundary of the given multivariate performance measure. The objective function is optimized with regard to classifier parameter and kernel weight alternately in an iterative algorithm by using cutting plane algorithm. The developed algorithm is evaluated on two different pattern classification methods with regard to various multivariate performance measure optimization problems. The experiment results show the proposed algorithm outperforms the competing methods.

关键词： Pattern recognition multiple kernel multivariate performance measures cutting plane algorithm

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A cutting plane algorithm for frequency domain specification with application to bending modes attenuation

A cutting plane algorithm for frequency domain specification...

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American Control Conference 2005 (ACC)

作者： Abbas-Turki, M Duc, G Font, S Clement, B Ecole Super Elect Serv Automat F-91192 Gif Sur Yvette France

ISBN: (纸本)0780390989

Bending modes attenuation is a very challenging problem, especially if the modes are close to the bandwidth, in which case applying weighting filters is useless. This work aims to present an idea based on the cutting plane algorithm (CPA) to overcome such problems. The interesting point of using CPA instead of optimization under LMI (Linear Matrix Inequality) constraints is that no additional variables are introduced, which has a significant effect on the computation time. The application of Youla parameterization is considered in order to restore the linearity in the compensator parameters, thus the convexity is guaranteed and the CPA is efficiently used. Keywords: Youla parameterization, cutting plane algorithm, KYP lemma.

关键词： Youla parameterization cutting plane algorithm KYP lemma

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An enhanced cutting plane algorithm of elastoplastic constitutive models for geomaterials

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COMPUTERS AND GEOTECHNICS 2023年第1期155卷

作者： Zhao, Lun-Yang Liu, Ling-Hui Lai, Yuan-Ming South China Univ Technol South China Inst Geotech Engn Sch Civil Engn & Transportat Guangzhou 510641 Peoples R China South China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510641 Peoples R China Chinese Acad Sci Northwest Inst Ecoenvironm & Resources State Key Lab Frozen Soil Engn Lanzhou 730000 Gansu Peoples R China

Integration of the nonlinear stress-strain relationship plays a critical role in the application of constitutive models to engineering practice. Aiming at the nonlinear integration problems commonly existing in elastoplastic constitutive models for geomaterials, we herein present a robust enhanced cutting plane algorithm (ECPA). This algorithm is based on the traditional cutting plane algorithm (CPA) with a new adaptive substepping technique. The accuracy of the CPA is first investigated via a series of numerical examples on a unified hardening/softening elastoplastic model with different nonlinearity degrees of yield functions and plastic potential functions. An intriguing observation is that the accuracy of CPA cannot be guaranteed as long as the plastic flow direction (i.e., partial derivative G/partial derivative sigma) is not a constant during loading. To overcome this deficiency, a substepping technique for adaptively restricting substep increments solely related to the plastic flow direction was originally proposed and embedded into CPA. The robustness, including the accuracy and efficiency of the proposed ECPA, is evaluated by setting different increment steps and error tolerances. Finally, the ECPA is applied to the Modified Cam Clay (MCC) model, and the robustness of the ECPA is further assessed in element scale tests and a boundary value problem.

关键词： Numerical integration cutting plane algorithm Adaptive substepping Elastoplastic models Modified Cam Clay

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A computational study of the cutting plane tree algorithm for general mixed-integer linear programs

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OPERATIONS RESEARCH LETTERS 2012年第1期40卷 15-19页

作者： Chen, Binyuan Kuecuekyavuz, Simge Sen, Suvrajeet Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA Ohio State Univ Data Driven Decis Lab Dept Integrated Syst Engn Columbus OH 43210 USA

The cutting plane tree algorithm provides a finite procedure for solving general mixed-integer linear programs with bounded integer variables. The computational evidence provided in this work illustrates that this algorithm is powerful enough to close a significant fraction of the integrality gap for moderately sized MIPLIB instances. (C) 2011 Elsevier B.V. All rights reserved.

关键词： cutting plane algorithm Multi-term disjunctions

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cutting plane algorithms for nonlinear semi-definite programming problems with applications

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JOURNAL OF GLOBAL OPTIMIZATION 2003年第2期25卷 141-155页

作者： Konno, H Kawadai, N Tuy, H Chuo Univ Dept Ind & Syst Engn Tokyo 112 Japan Tokyo Inst Technol Dept Ind Engn & Management Tokyo 152 Japan Inst Math Hanoi 10000 Vietnam

We will propose an outer-approximation (cutting plane) method for minimizing a function f(X) subject to semi-definite constraints on the variables X is an element of R-nxn. A number of efficient algorithms have been proposed when the objective function is linear. However, there are very few practical algorithms when the objective function is nonlinear. An algorithm to be proposed here is a kind of outer-approximation( cutting plane) method, which has been successfully applied to several low rank global optimization problems including generalized convex multiplicative programming problems and generalized linear fractional programming problems, etc. We will show that this algorithm works well when f is convex and n is relatively small. Also, we will provide the proof of its convergence under various technical assumptions.

关键词： semi-definite programming low rank nonconvex problem cutting plane algorithm outer-approximation semi-infinite programming ellipsoidal separation quadratic regression semidefinite logit model

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STABILITY ANALYSIS OF DISCRETE-TIME LINEAR COMPLEMENTARITY SYSTEMS

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SIAM JOURNAL ON OPTIMIZATION 2025年第1期35卷 419-444页

作者： Raghunathan, Arvind u. Linderoth, Jeffrey t. Mitsubishi Elect Res Labs Cambridge MA 02139 USA Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA

A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient conditions for Lyapunov stability of a DLCS when using a quadratic Lyapunov function that depends only on the state variables and a quadratic Lyapunov function that depends both on the state and the algebraic variables. The sufficient conditions require checking the feasibility of a copositive program over nonconvex cones. Our results only assume that the LCP is solvable and do not require the solutions to be unique. We devise a novel, exact cutting plane algorithm for the verification of stability and the computation of the Lyapunov functions. To the best of our knowledge, our algorithm is the first exact approach for stability verification of DLCS. A number of numerical examples are presented to illustrate the approach. Though our main object of study in this paper is the DLCS, the proposed algorithm can be readily applied to the stability verification of LCS. In this context, we show the equivalence between the stability of a LCS and the DLCS, resulting from a time-stepping procedure applied to the LCS for all sufficiently small time steps.

关键词： Lyapunov stability common quadratic Lyapunov function extended quadratic Lyapunov function copositive program cutting plane algorithm

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cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs

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COMPUTATIONAL MANAGEMENT SCIENCE 2015年第2期12卷 319-340页

作者： Takano, Yuichi Nanjo, Keisuke Sukegawa, Noriyoshi Mizuno, Shinji Senshu Univ Sch Network & Informat Tama Ku 2-1-1 Higashimita Kawasaki Kanagawa 2148580 Japan Tokyo Inst Technol Dept Ind Engn & Management Meguro Ku Tokyo 1528552 Japan Tokyo Inst Technol Dept Ind Engn & Management Meguro Ku Tokyo 1528552 Japan

This paper studies the mean-risk portfolio optimization problem with nonconvex transaction costs. We employ the conditional value-at-risk (CVaR) as a risk measure. There are a number of studies that aim at efficiently solving large-scale CVaR minimization problems. None of these studies, however, take into account nonconvex transaction costs, which are present in practical situations. To make a piecewise linear approximation of the transaction cost function, we utilized special ordered set type two constraints. Moreover, we devised a subgradient-based cutting plane algorithm to handle a large number of scenarios. This cutting plane algorithm needs to solve a mixed integer linear programming problem in each iteration, and this requires a substantial computation time. Thus, we also devised a two-phase cutting plane algorithm that is even more efficient. Numerical experiments demonstrated that our algorithms can attain near-optimal solutions to large-scale problems in a reasonable amount of time. Especially when rebalancing a current portfolio that is close to an optimal one, our algorithms considerably outperform other solution methods.

关键词： Portfolio optimization Conditional value-at-risk cutting plane algorithm Transaction costs Mixed integer linear programming

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A cutting plane approach to combinatorial bandwidth packing problem with queuing delays

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OPTIMIZATION LETTERS 2017年第1期11卷 225-239页

作者： Jayaswal, Sachin Vidyarthi, Navneet Das, Sagnik Indian Inst Management Ahmedabad Prod & Quantitat Methods Ahmadabad Gujarat India Concordia Univ John Molson Sch Business Dept Supply Chain & Business Technol Management Montreal PQ Canada Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

The combinatorial bandwidth packing problem (CBPP), arising in a telecommunication network with limited bandwidth, is defined as follows. Given a set of requests, each with its potential revenue, and each consisting of calls with their bandwidth requirements, decide: (1) a subset of the requests to accept/reject;and (2) a route for each call in accepted requests, so as to maximize the total revenue earned in a telecommunication network with limited bandwidth. However, telecommunication networks are generally characterized by variability in the call (bits) arrival rates and service times, resulting in queuing delays in the network. In this paper, we present a non-linear integer programming model to account for such delays in CBPP. Using simple transformation and piecewise outer-approximation, we reformulate the model as a linear mixed integer program (MIP), but with a large number of constraints. We present an efficient cutting plane approach to solve the resulting linear MIP to epsilon-optimality.

关键词： OR in telecommunications Bandwidth packing Integer programming Queueing cutting plane algorithm

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cutting-plane-based algorithms for two branch vertices related spanning tree problems

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OPTIMIZATION AND ENGINEERING 2014年第4期15卷 855-887页

作者： Rossi, Andre Singh, Alok Sundar, Shyam Univ Bretagne Sud Lab STICC CNRS F-56321 Lorient France Univ Hyderabad Dept Comp & Informat Sci Hyderabad 500046 Andhra Pradesh India

A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier.

关键词： Spanning tree Branch vertex cutting plane algorithm Matheuristic Tabu search Wavelength-division

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