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A VU-decomposition method for a second-order cone programming problem
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作者 陆媛 庞丽萍 夏尊铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第2期263-270,共8页
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi... A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given. 展开更多
关键词 second-order cone programming nonsmooth optimization vu-Lagrangian vu-decomposition
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Anti-interference beam pattern design based on second-order cone programming optimization 被引量:1
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作者 戴文舒 鲍凯凯 +1 位作者 王萍 王黎明 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2016年第3期255-260,共6页
When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be op... When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization (SOCP) algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming. 展开更多
关键词 anti-interference beam pattern second-order cone programming optimization (SOCP) weak signal detection
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Improved design of reconfigurable frequency response masking filters based on second-order cone programming
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作者 吴尘 徐新洲 +1 位作者 黄程韦 赵力 《Journal of Southeast University(English Edition)》 EI CAS 2014年第4期422-427,共6页
In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that se... In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method. 展开更多
关键词 frequency response masking FRM filter optimal design reconfigurability second-order cone programming SOCP
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Two new predictor-corrector algorithms for second-order cone programming 被引量:1
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作者 曾友芳 白延琴 +1 位作者 简金宝 唐春明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第4期521-532,共12页
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algor... Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(εo/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective. 展开更多
关键词 second-order cone programming infeasible interior-point algorithm predictor-corrector algorithm global convergence complexity analysis
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Robust Blind Separation for MIMO Systems against Channel Mismatch Using Second-Order Cone Programming 被引量:1
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作者 Zhongqiang Luo Chengjie Li Lidong Zhu 《China Communications》 SCIE CSCD 2017年第6期168-178,共11页
To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple... To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem. 展开更多
关键词 multiple-input multiple-output channel mismatch second-order cone programming blind source separation independent component analysis
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AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM 被引量:11
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作者 迟晓妮 刘三阳 《Acta Mathematica Scientia》 SCIE CSCD 2008年第3期551-559,共9页
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh- Haeberly-Overton (AHO) search direction. This algorith... A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh- Haeberly-Overton (AHO) search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O(√n ln(ε0/ε)) iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP. 展开更多
关键词 second-order cone programming infeasible-interior-point algorithm predictor-corrector algorithm global convergence
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POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 LI Ren-gui(李仁贵) +1 位作者 LI Li-shan(刘立山) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第4期495-500,共6页
New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the cond... New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory. 展开更多
关键词 second-order singular boundary value problems positive solutions cone fixed point
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Positive Solutions for a Class of Second-order m-point Boundary Value Problems
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作者 YAN Jie-sheng YANG Liu LIU Xi-ping 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第3期448-454,共7页
Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive... Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given. 展开更多
关键词 second-order m-point boundary value problem fixed point cone positive solution
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SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH 被引量:8
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作者 迟晓妮 韦洪锦 +1 位作者 万仲平 朱志斌 《Acta Mathematica Scientia》 SCIE CSCD 2017年第5期1262-1280,共19页
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w... In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP. 展开更多
关键词 circular cone programming second-order cone programming nonmonotone line search smoothing Newton method local quadratic convergence
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Exact Computable Representation of Some Second-Order Cone Constrained Quadratic Programming Problems 被引量:1
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作者 Qingwei Jin Ye Tian +2 位作者 Zhibin Deng Shu-Cherng Fang Wenxun Xing 《Journal of the Operations Research Society of China》 EI 2013年第1期107-134,共28页
Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a noncon... Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints. 展开更多
关键词 Linear conic program Semidefinite program Nonconvex quadratically constrained quadratic program second-order cone
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Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB 被引量:2
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作者 Qi Li Zhiping Qiu Xudong Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2015年第6期845-854,共10页
In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints (the DCA for QB), a new method is proposed to solve the... In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints (the DCA for QB), a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods. 展开更多
关键词 Interval parameters · second-order Taylorseries expansion · Static response of uncertain structures Quadratic programming problems · DCA
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Day-ahead Optimization Schedule for Gas-electric Integrated Energy System Based on Second-order Cone Programming 被引量:26
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作者 Yonghui Sun Bowen Zhang +3 位作者 Leijiao Ge Denis Sidorov Jianxi Wang Zhou Xu 《CSEE Journal of Power and Energy Systems》 SCIE CSCD 2020年第1期142-151,共10页
This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas sy... This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES. 展开更多
关键词 Day-ahead optimization schedule integrated energy system natural gas system second-order cone programming
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Optimal design and verification of temporal and spatial filters using second-order cone programming approach 被引量:7
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作者 YAN Shefeng MA Yuanliang 《Science in China(Series F)》 2006年第2期235-253,共19页
Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also... Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming (SOCP) and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach. 展开更多
关键词 filter design beamformer design spatial filter design second-order cone programming.
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Nonsingularity in second-order cone programming via the smoothing metric projector 被引量:1
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作者 WANG Yun 1,& ZHANG LiWei 2 1 College of Information Sciences and Engineering,Shandong Agricultural University,Tai’an 271018,China 2 Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China 《Science China Mathematics》 SCIE 2010年第4期1025-1038,共14页
Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of... Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition. 展开更多
关键词 second-order cone programming problem SMOOTHING METRIC PROJECTOR B-subdifferential Clarke’s generalized JACOBIAN SMOOTHING Newton method
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A New Complementarity Function and Applications in Stochastic Second-Order Cone Complementarity Problems 被引量:1
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作者 Guo Sun Jin Zhang +1 位作者 Li-Ying Yu Gui-Hua Lin 《Journal of the Operations Research Society of China》 EI CSCD 2019年第2期251-283,共33页
This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual com... This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks. 展开更多
关键词 Stochastic second-order cone complementarity problem Complementarity function Expected Residual Minimization(ERM)model Monte Carlo method Error bound Optimal power flow
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A Class of Second-Order Cone Eigenvalue Complementarity Problems for Higher-Order Tensors
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作者 Jiao-Jiao Hou Chen Ling Hong-Jin He 《Journal of the Operations Research Society of China》 EI CSCD 2017年第1期45-64,共20页
In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under consideration.Specifically,for the general SOCTEiCP,we ... In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under consideration.Specifically,for the general SOCTEiCP,we first show its equivalence to a particular variational inequality under reasonable conditions.A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the problem.Then,for the symmetric and sub-symmetric SOCTEiCPs,we reformulate them as appropriate nonlinear programming problems,which are extremely beneficial for designing reliable solvers to find solutions of the considered problem.Finally,we report some preliminary numerical results to verify our theoretical results. 展开更多
关键词 Higher-order tensor Eigenvalue complementarity problem Tensor complementarity problem second-order cone Variational inequality Polynomial optimization
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A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics 被引量:1
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作者 Liang Wang Xue Zhang +1 位作者 Jingjing Meng Qinghua Lei 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2172-2183,共12页
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene... In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics. 展开更多
关键词 Particle finite element method Nodal integration Dynamic saturated media second-order cone programming(SOCP)
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Existence of Positive Solutions for Singular Second-order m-Point Boundary Value Problems 被引量:23
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作者 Guo-weiZhang Jing-xianSun 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第4期655-664,共10页
The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (L&#981;)(x) = (p(x)&#981;&#8242... The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (L&#981;)(x) = (p(x)&#981;&#8242;(x))&#8242; + q(x)&#981;(x) and &#958;<SUB> i </SUB>&#8712; (0, 1) with 0 【 &#958;<SUB>1</SUB> 【 &#958;<SUB>2</SUB> 【 · · · 【 &#958;<SUB> m&#8722;2</SUB> 【 1, a <SUB>i </SUB>&#8712; [0, &#8734;). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions. 展开更多
关键词 second-order singular equation multi-point boundary value problem positive solution cone fixed point index
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Higher-order Symmetric Duality in Multiobjective Programming Problems 被引量:2
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作者 Ying GAO 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期485-494,共10页
In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse dual... In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order (strongly) cone pseudoinvexity assumptions. 展开更多
关键词 multiobjective programming problems higher-order symmetric duality higher-order cone pseu-doinvex functions
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Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming
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作者 Liang Chen Junyuan Zhu Xinyuan Zhao 《Science China Mathematics》 SCIE CSCD 2022年第11期2397-2422,共26页
In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.S... In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.Specifically,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the multipliers.We first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity fails.Subsequently,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity. 展开更多
关键词 second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming
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