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Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function 被引量:9
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作者 Yan Qin BAI Guo Qiang WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第11期2027-2042,共16页
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and qu... A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(√Nlog N log N/ε) for large-update methods and O(√Nlog N/ε) for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q. 展开更多
关键词 second-order cone optimization linear optimization interior-point methods large- and small-update methods polynomial-time complexity
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A Modified and Simplified Full Nesterov–Todd Step O(N)Infeasible Interior-Point Method for Second-Order Cone Optimization
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作者 Behrouz Kheirfam 《Journal of the Operations Research Society of China》 EI CSCD 2018年第2期301-315,共15页
We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iterat... We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods. 展开更多
关键词 second-order cone optimization Infeasible interior-point method Primal-dual method Polynomial complexity
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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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On Second-order Sufficient Conditions in Constrained Nonsmooth Optimization
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作者 WANG FENG-LING SONG WEN Li Yong 《Communications in Mathematical Research》 CSCD 2010年第3期203-210,共8页
In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d... In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113(2008), 283-298] to constrained optimization problems. 展开更多
关键词 second-order optimality condition g-stable function Dini directional derivative isolated minimizer
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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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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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CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION 被引量:10
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作者 丘京辉 《Acta Mathematica Scientia》 SCIE CSCD 2007年第1期211-218,共8页
By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
关键词 Preinvex set-valued optimization cone-directed contingent derivative optimality conditions
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Interactive Evolutionary Multi-Objective Optimization Algorithm Using Cone Dominance
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作者 Dalaijargal Purevsuren Saif ur Rehman +2 位作者 Gang Cui Jianmin Bao Nwe Nwe Htay Win 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2015年第6期76-84,共9页
As the number of objectives increases,the performance of the Pareto dominance-based Evolutionary Multi-objective Optimization( EMO) algorithms such as NSGA-II,SPEA2 severely deteriorates due to the drastic increase in... As the number of objectives increases,the performance of the Pareto dominance-based Evolutionary Multi-objective Optimization( EMO) algorithms such as NSGA-II,SPEA2 severely deteriorates due to the drastic increase in the Pareto-incomparable solutions. We propose a sorting method which classifies these incomparable solutions into several ordered classes by using the decision maker's( DM) preference information.This is accomplished by designing an interactive evolutionary algorithm and constructing convex cones. This method allows the DMs to drive the search process toward a preferred region of the Pareto optimal front. The performance of the proposed algorithm is assessed for two,three,and four-objective knapsack problems. The results demonstrate the algorithm ' s ability to converge to the most preferred point. The evaluation and comparison of the results indicate that the proposed approach gives better solutions than that of NSGA-II. In addition,the approach is more efficient compared to NSGA-II in terms of the number of generations required to reach the preferred point. 展开更多
关键词 multi-objective optimization evolutionary optimization preference information pareto dominance cone dominance
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Feasibility and Structural Feature on Monotone Second-Order Cone Linear Complementarity Problems in Hilbert Space
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作者 苗新河 郭胜娟 《Transactions of Tianjin University》 EI CAS 2015年第4期377-382,共6页
Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the... Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected. 展开更多
关键词 second-order cone linear complementarity JORDAN frame JORDAN product Lorentz cone ADJOINT operator
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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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Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones
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作者 S. K. Suneja Sunila Sharma Malti Kapoor 《Applied Mathematics》 2015年第1期7-19,共13页
In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduc... In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established. 展开更多
关键词 NONSMOOTH Vector optimization OVER coneS (Weak) MINIMIZERS of Order k NONSMOOTH (F ρ)-Convex Function of Order k
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Optimal Multiperiodic Control for Inventory Coupled Systems: A Multifrequency Second-Order Test
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作者 Marek Skowron Krystyn Styczeń 《Open Journal of Optimization》 2016年第3期91-101,共12页
A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products b... A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented. 展开更多
关键词 optimal Multiperiodic Control Complex Systems Inventory Interactions Nested optimization Multifrequency second-order Test
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A Different Approach to Cone-Convex Optimization
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作者 Surjeet Kaur Suneja Sunila Sharma +1 位作者 Meetu B. Grover Malti Kapoor 《American Journal of Operations Research》 2013年第6期536-541,共6页
In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently... In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established. 展开更多
关键词 CONVEX optimization cone-Convex FUNCTIONS KKT Conditions DUALITY
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Multiconstraint adaptive three-dimensional guidance law using convex optimization 被引量:6
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作者 FU Shengnan LIU Xiaodong +1 位作者 ZHANG Wenjie XIA Qunli 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第4期791-803,共13页
The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional na... The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications. 展开更多
关键词 proportional navigation(PN) adaptive guidance law three-dimensional space second-order cone programming(SOCP) convex optimal control
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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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Advanced algorithms for retrieving pileup peaks of digital alpha spectroscopy using antlions and particle swarm optimizations 被引量:1
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作者 Mohamed S.El_Tokhy 《Nuclear Science and Techniques》 SCIE CAS CSCD 2020年第4期47-68,共22页
Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)alg... Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate. 展开更多
关键词 ALPHA SPECTROMETRY instrument second-order pileup SIGNAL processing optimization algorithms
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On super efficiency in set-valued optimization 被引量:3
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作者 LI Tai-yong XU Yi-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第2期144-150,共7页
The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperatio... The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker's, Lagrange's and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker's, Lagrange's and saddle points optimality conditions are derived. 展开更多
关键词 super efficiency IC-cone-CONVEXLIKENESS set-valued optimization saddle point
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Time-optimal rendezvous transfer trajectory for restricted cone-angle range solar sails 被引量:1
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作者 Jing He Sheng-Ping Gong +1 位作者 Fang-Hua Jiang Jun-Feng Li 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第5期628-635,共8页
The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In additio... The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In addition, the solar radiation pressure force is also related to the solar sail orientation with respect to the sunlight direction. For an ideal flat solar sail, the cone angle between the sail normal and the sunlight direction determines the magnitude and direction of solar radiation pressure force. In general, the cone angle can change from 0° to 90°. However, in practical applications, a large cone angle may reduce the efficiency of solar radiation pressure force and there is a strict requirement on the attitude control. Usually, the cone angle range is restricted less more than an acute angle (for example, not more than 40°) in engineering practice. In this paper, the time-optimal transfer trajectory is designed over a restricted range of the cone angle, and an indirect method is used to solve the two point boundary value problem associated to the optimal control problem. Relevant numerical examples are provided to compare with the case of an unrestricted case, and the effects of different maximum restricted cone angles are discussed. The results indicate that (1) for the condition of a restricted cone-angle range the transfer time is longer than that for the unrestricted case and (2) the optimal transfer time increases as the maximum restricted cone angle decreases. 展开更多
关键词 Solar sail - Time-optimal rendezvous Indirect method Restricted cone-angle range
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