Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields ...Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.展开更多
Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with si...Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.展开更多
We propose a new two-phase method for reconstruction of blurred im-ages corrupted by impulse noise.In the first phase,we use a noise detector to iden-tify the pixels that are contaminated by noise,and then,in the seco...We propose a new two-phase method for reconstruction of blurred im-ages corrupted by impulse noise.In the first phase,we use a noise detector to iden-tify the pixels that are contaminated by noise,and then,in the second phase,we reconstruct the noisy pixels by solving an equality constrained total variation mini-mization problem that preserves the exact values of the noise-free pixels.For images that are only corrupted by impulse noise(i.e.,not blurred)we apply the semismooth Newton’s method to a reduced problem,and if the images are also blurred,we solve the equality constrained reconstruction problem using a first-order primal-dual algo-rithm.The proposed model improves the computational efficiency(in the denoising case)and has the advantage of being regularization parameter-free.Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.展开更多
In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the ...In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.展开更多
In this paper,we propose a randomized primal–dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints.Assuming mere ...In this paper,we propose a randomized primal–dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints.Assuming mere convexity,we establish its O(1/t)convergence rate in terms of the objective value and feasibility measure.The framework includes several existing algorithms as special cases such as a primal–dual method for bilinear saddle-point problems(PD-S),the proximal Jacobian alternating direction method of multipliers(Prox-JADMM)and a randomized variant of the ADMM for multi-block convex optimization.Our analysis recovers and/or strengthens the convergence properties of several existing algorithms.For example,for PD-S our result leads to the same order of convergence rate without the previously assumed boundedness condition on the constraint sets,and for Prox-JADMM the new result provides convergence rate in terms of the objective value and the feasibility violation.It is well known that the original ADMM may fail to converge when the number of blocks exceeds two.Our result shows that if an appropriate randomization procedure is invoked to select the updating blocks,then a sublinear rate of convergence in expectation can be guaranteed for multi-block ADMM,without assuming any strong convexity.The new approach is also extended to solve problems where only a stochastic approximation of the subgradient of the objective is available,and we establish an O(1/√t)convergence rate of the extended approach for solving stochastic programming.展开更多
Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to...Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.展开更多
Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for sol...Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.展开更多
This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the...This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the help of projection operators,a primal-dual framework,and Nesterov's accelerated method,we first design a distributed accelerated primal-dual projection neurodynamic approach(DAPDP),and its convergence rate of the primal-dual gap is O(1/(t^(2)))by selecting appropriate parameters and initial values.Then,when the local closed convex sets are convex inequalities which have no closed-form solutions of their projection operators,we further propose a distributed accelerated penalty primal-dual neurodynamic approach(DAPPD)on the strength of the penalty method,primal-dual framework,and Nesterov's accelerated method.Based on the above analysis,we prove that DAPPD also has a convergence rate O(1/(t^(2)))of the primal-dual gap.Compared with the distributed dynamical approaches based on the classical primal-dual framework,our proposed distributed accelerated neurodynamic approaches have faster convergence rates.Numerical simulations demonstrate that our proposed neurodynamic approaches are feasible and effective.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos.10771133 and 70871082)Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10117733）, the Shanghai Leading Academic Discipline Project （Grant No.J50101）, and the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai （Grant No.06XPYQ52）
文摘Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.
基金The work of Y.Dong is supported by Advanced Grant No.291405 from the European Research Council.
文摘We propose a new two-phase method for reconstruction of blurred im-ages corrupted by impulse noise.In the first phase,we use a noise detector to iden-tify the pixels that are contaminated by noise,and then,in the second phase,we reconstruct the noisy pixels by solving an equality constrained total variation mini-mization problem that preserves the exact values of the noise-free pixels.For images that are only corrupted by impulse noise(i.e.,not blurred)we apply the semismooth Newton’s method to a reduced problem,and if the images are also blurred,we solve the equality constrained reconstruction problem using a first-order primal-dual algo-rithm.The proposed model improves the computational efficiency(in the denoising case)and has the advantage of being regularization parameter-free.Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.
文摘In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.
基金This work is partly supported by the National Science Foundation(Nos.DMS-1719549 and CMMI-1462408).
文摘In this paper,we propose a randomized primal–dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints.Assuming mere convexity,we establish its O(1/t)convergence rate in terms of the objective value and feasibility measure.The framework includes several existing algorithms as special cases such as a primal–dual method for bilinear saddle-point problems(PD-S),the proximal Jacobian alternating direction method of multipliers(Prox-JADMM)and a randomized variant of the ADMM for multi-block convex optimization.Our analysis recovers and/or strengthens the convergence properties of several existing algorithms.For example,for PD-S our result leads to the same order of convergence rate without the previously assumed boundedness condition on the constraint sets,and for Prox-JADMM the new result provides convergence rate in terms of the objective value and the feasibility violation.It is well known that the original ADMM may fail to converge when the number of blocks exceeds two.Our result shows that if an appropriate randomization procedure is invoked to select the updating blocks,then a sublinear rate of convergence in expectation can be guaranteed for multi-block ADMM,without assuming any strong convexity.The new approach is also extended to solve problems where only a stochastic approximation of the subgradient of the objective is available,and we establish an O(1/√t)convergence rate of the extended approach for solving stochastic programming.
基金Supported in part by the NNSF of China(11301129,11271323,91330105,11326033)the Zhejiang Provincial Natural Science Foundation of China(LQ13A010025,LZ13A010002)
文摘Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.
基金This research was supported by the National Natural Science Foundation of China(Nos.71471112 and 71871140).
文摘Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.
基金supported by the National Natural Science Foundation of China (Grant No.62176218)the Fundamental Research Funds for the Central Universities (Grant No.XDJK2020TY003)。
文摘This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the help of projection operators,a primal-dual framework,and Nesterov's accelerated method,we first design a distributed accelerated primal-dual projection neurodynamic approach(DAPDP),and its convergence rate of the primal-dual gap is O(1/(t^(2)))by selecting appropriate parameters and initial values.Then,when the local closed convex sets are convex inequalities which have no closed-form solutions of their projection operators,we further propose a distributed accelerated penalty primal-dual neurodynamic approach(DAPPD)on the strength of the penalty method,primal-dual framework,and Nesterov's accelerated method.Based on the above analysis,we prove that DAPPD also has a convergence rate O(1/(t^(2)))of the primal-dual gap.Compared with the distributed dynamical approaches based on the classical primal-dual framework,our proposed distributed accelerated neurodynamic approaches have faster convergence rates.Numerical simulations demonstrate that our proposed neurodynamic approaches are feasible and effective.
