In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure betwe...In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.展开更多
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr...In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.展开更多
A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Un...A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.展开更多
In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps....In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.展开更多
This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the fea...This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.展开更多
When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of...When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.展开更多
This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the fo...This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recur- sively defined reproducing kernels. As an application, we get a recursive Neville-Aitken- type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.展开更多
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
基金Supported by the Natural Science Foundation of Hubei Province(2008CDZD47)
文摘In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.
基金Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
文摘In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.
文摘In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)Scientific Research Project of Hezhou University(Grant Nos.2014YBZK06 and 2016HZXYSX03)
文摘This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579038 and 51490672)the National Basic Research Program of China(Grant No.2013CB036101)
文摘When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.
文摘This paper is an extension of earlier papers [8, 9] on the ＂native＂ Hilbert spaces of functions on some domain Ωbelong toR^d Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recur- sively defined reproducing kernels. As an application, we get a recursive Neville-Aitken- type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
