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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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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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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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Smoothing Newton Algorithm for Linear Programming over Symmetric Cones 被引量:1
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作者 刘晓红 倪铁 《Transactions of Tianjin University》 EI CAS 2009年第3期216-221,共6页
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algor... By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra smoothing algorithm
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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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On Second-Order Duality in Nondifferentiable Continuous Programming 被引量:1
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作者 I. Husain Santosh K. Shrivastav 《American Journal of Operations Research》 2012年第3期289-295,共7页
A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-i... A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature. 展开更多
关键词 Continuous programMING second-order INVEXITY second-order PSEUDOINVEXITY second-order Quasi-Invexity second-order DUALITY Nonlinear programMING
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Polynomial Complexity Bounds of Mehrotra-type Predictor-corrector Algorithms for Linear Programming over Symmetric Cones
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作者 刘长河 尚有林 李振国 《Chinese Quarterly Journal of Mathematics》 2015年第4期475-494,共20页
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s... We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O(r log ε1) iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra interior-point methods Mehrotra-type algorithm polynomial complexity
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Second-Order Duality for Continuous Programming Containing Support Functions
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作者 Iqbal Husain Mashoob Masoodi 《Applied Mathematics》 2010年第6期534-541,共8页
A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order in... A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined. 展开更多
关键词 Continuous programMING second-order INVEXITY second-order PSEUDOINVEXITY second-order DUALITY Nonlinear programMING Support Functions Natural Boundary VALUES
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Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices
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作者 Caiyun Jin Cao-Zong Cheng 《Applied Mathematics》 2011年第11期1387-1392,共6页
Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related gen... Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I. 展开更多
关键词 HIGHER-ORDER (F α p d b φ Vector-Pseudoquasi-Type I HIGHER-ORDER DUALITY MINIMAX FRACTIONAL TYPE programMING Positive Semidefinite symmetric Matrix
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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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Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems
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作者 I. Husain Vikas K. Jain 《American Journal of Operations Research》 2012年第4期536-545,共10页
Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type s... Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature. 展开更多
关键词 NONDIFFERENTIABLE MULTIOBJECTIVE programMING second-order INVEXITY second-order Pseudoinvexity second-order Quasi-Invexity second-order DUALITY Nonlinear MULTIOBJECTIVE programMING
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The Second-Order Differential Equation System with the Feedback Controls for Solving Convex Programming
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作者 Xingxu Chen Li Wang +1 位作者 Juhe Sun Yanhong Yuan 《Open Journal of Applied Sciences》 2022年第6期977-989,共13页
In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent opera... In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem. 展开更多
关键词 Convex programming Lagrange Function Projection Operator second-order Differential Equation
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An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface 被引量:2
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作者 Chein-Shan Liu Bo-Tong Li 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第1期228-241,I0007,共15页
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ... A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces. 展开更多
关键词 symmetric composite beams R(x)-orthogonality of second-order derivatives of boundary functions R(x)-orthonormal THEORY Non-smooth/discontinuous interface Sequentially closed-from natural frequencies
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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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AN ITERATED-SUBSPACEMINIMIZATION METHODS WITHSYMMETRIC RANK-ONE UPDATING 被引量:1
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作者 徐徽宁 孙麟平 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2004年第2期233-240,共8页
We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems. At each major iteration of the method,a two-dimensional manifold, the iterated subspace, is constr... We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems. At each major iteration of the method,a two-dimensional manifold, the iterated subspace, is constructed and an approximate minimizer of the objective function in this manifold then determined, and a symmetric rank-one updating is used to solve the inner minimization problem. 展开更多
关键词 大型无约束最优化 迭代子空间最小化 无约束规划 对称秩单较正
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Multiobjective Nonlinear Symmetric Duality Involving Generalized Pseudoconvexity
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作者 Mohamed Abd El-Hady Kassem 《Applied Mathematics》 2011年第10期1236-1242,共7页
The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functi... The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theorems for this pair are established. Finally, a self duality theorem is given. 展开更多
关键词 MULTIOBJECTIVE programming second-order symmetric Dual Models DUALITY THEOREMS PSEUDOCONVEX Functions CONES
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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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一类对称可微不变凸多目标规划的最优性
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作者 张媛 李钰 《贵州大学学报(自然科学版)》 2024年第2期9-14,共6页
多目标规划与广义凸性是最优化理论的重要研究内容。主要利用Minch对称梯度,定义了一类对称可微G-B s-(p,r,ρ)不变凸函数,利用该函数建立了含有不等式约束的多目标规划问题,并证明了该函数凸性限制下的最优性充分条件,进一步拓宽了涉及... 多目标规划与广义凸性是最优化理论的重要研究内容。主要利用Minch对称梯度,定义了一类对称可微G-B s-(p,r,ρ)不变凸函数,利用该函数建立了含有不等式约束的多目标规划问题,并证明了该函数凸性限制下的最优性充分条件,进一步拓宽了涉及B-(p,r)不变凸函数、G-ρ不变凸函数的文献中有关最优性条件的结论。 展开更多
关键词 Minch对称梯度 G-B s-(p r ρ)不变凸函数 多目标规划 最优性条件 有效解
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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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