In this paper, a corrector-predictor interior-point algorithm is proposed for sym- metric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-p...In this paper, a corrector-predictor interior-point algorithm is proposed for sym- metric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iter- ates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algo- rithm is shown and it is proved that the algorithm has the complexity bound O （√τL） for the well-known Nesterov-Todd search direction and O （τL） for the xs and sx search directions.展开更多
In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a f...In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a full Nesterov-Todd step and the strategy of the central path to obtain a solution of symmetric optimization.We establish the iteration bound for the algorithm,which matches the currently best-known iteration bound for these methods,and prove that the algorithm is quadratically convergent.展开更多
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
this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The converg...this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The convergence is shown for commutative class of search directions.Moreover,we analyze the algorithm and obtain the complexity bounds,which coincide with the best-known results for the Cartesian P_(∗)(κ)-SCLCPs.Some numerical tests are reported to illustrate our theoretical results.展开更多
A finite impulse-response microwave photonic filter is typically achieved based on spectrum-shaped optical frequency combs and a dispersive element. We propose an analytical model to describe the amplitude responses o...A finite impulse-response microwave photonic filter is typically achieved based on spectrum-shaped optical frequency combs and a dispersive element. We propose an analytical model to describe the amplitude responses of the sidelobes. The model shows that the sidelobe suppression ratio is limited by the spectrum structure of the optical combs. By taking Gaussian-profiled combs as an example, it is both theoretically and experimentally proved that the suppression ratio can be improved by optimizing the spectral power range, which is defined as the ratio of the maximum tap weight to the minimum tap weight.展开更多
基金Shahrekord University for financial supportpartially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran
文摘In this paper, a corrector-predictor interior-point algorithm is proposed for sym- metric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iter- ates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algo- rithm is shown and it is proved that the algorithm has the complexity bound O （√τL） for the well-known Nesterov-Todd search direction and O （τL） for the xs and sx search directions.
基金The author is grateful to the two anonymous referees and the Editors for theirconstructive comments and suggestions to improve the presentation.
文摘In this paper a weighted short-step primal-dual interior-point algorithm for linear optimization over symmetric cones is proposed that uses new search directions.The algorithm uses at each interior-point iteration a full Nesterov-Todd step and the strategy of the central path to obtain a solution of symmetric optimization.We establish the iteration bound for the algorithm,which matches the currently best-known iteration bound for these methods,and prove that the algorithm is quadratically convergent.
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The authors were partially supported by the Center of Excellence for Mathematics,University of Shahrekord,Shahrekord,Iran.
文摘this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The convergence is shown for commutative class of search directions.Moreover,we analyze the algorithm and obtain the complexity bounds,which coincide with the best-known results for the Cartesian P_(∗)(κ)-SCLCPs.Some numerical tests are reported to illustrate our theoretical results.
基金supported by National"973"Program of China(Nos.2012CB315603 and 2012CB315604)the National Natural Science Foundation of China(Nos.61321004,61420106003,and 61427813)
文摘A finite impulse-response microwave photonic filter is typically achieved based on spectrum-shaped optical frequency combs and a dispersive element. We propose an analytical model to describe the amplitude responses of the sidelobes. The model shows that the sidelobe suppression ratio is limited by the spectrum structure of the optical combs. By taking Gaussian-profiled combs as an example, it is both theoretically and experimentally proved that the suppression ratio can be improved by optimizing the spectral power range, which is defined as the ratio of the maximum tap weight to the minimum tap weight.
