Weighted Variational Minimization Model for Wavelet Domain Inpainting with Primal-Dual Method

To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.

A class of polynomial primal-dual interior-point algorithms for semidefinite optimization

In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely.

Distributed accelerated primal-dual neurodynamic approaches for resource allocation problem

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.

On Iteration Complexity of a First-Order Primal-Dual Method for Nonlinear Convex Cone Programming

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.

Adaptive Parallel Primal-Dual Method for Saddle Point Problems

The primal-dual hybrid gradient method is a classic way to tackle saddle-point problems.However,its convergence is not guaranteed in general.Some restric-tions on the step size parameters,e.g.,τσ≤1/||A^(T)A||,are imposed to guarantee the convergence.In this paper,a new convergent method with no restriction on parame-ters is proposed.Hence the expensive calculation of ||A^(T)A|| is avoided.This method produces a predictor like other primal-dual methods but in a parallel fashion,which has the potential to speed up the method.This new iterate is then updated by a sim-ple correction to guarantee the convergence.Moreover,the parameters are adjusted dynamically to enhance the efficiency as well as the robustness of the method.The generated sequence monotonically converges to the solution set.A worst-case O(1/t)convergence rate in ergodic sense is also established under mild assumptions.The nu-merical efficiency of the proposed method is verified by applications in LASSO problem and Steiner tree problem.

电动汽车规模化接入配电网的充电优化

将配变台区下的电动汽车看成一个小型"集聚体",提出基于配电网安全运行的充电优化问题模型,该模型以有功网损最小为目标函数,计及节点电压、线路潮流、配变容量、集中式充电功率的动态爬升约束以及充电能量平衡约束,优化慢充模式下"集聚体"的充电功率。分区代理商负责监控所管辖台区下每辆汽车的充电行为。采用原-对偶内点法求解该模型,IEEE 33节点系统、PG&E 69系统以及一个实际的119节点配电系统的计算结果表明该算法具有良好的收敛性和优化效果。通过动态平衡充电负荷,有效降低了系统网损,平抑了负荷波动,改善了末端电压水平,且避免了随机充电在某些时段可能造成的短时电压质量下降、馈线重载及配变过载等问题,提高了配电网运行的经济性和安全性。

计及碳排放含有碳捕集电厂电网的多目标动态最优潮流

为满足节能减排的要求,在碳捕集电厂的背景下,建立兼顾CO2排放和有功网损的多目标动态最优潮流模型。用模糊集理论将多目标优化问题转化为求取满意度最大的单目标问题,用内点法进行求解。对IEEE-30节点6机系统进行算例仿真,结果表明所提出的多目标动态最优潮流模型,可以在兼顾网损的同时减少CO2的排放,验证了模型的有效性。

用于改进潮流计算中PV-PQ节点类型转换逻辑的非线性规划模型

由于无功容量的限制,电力系统潮流计算中经常要进行PV-PQ节点类型转换,传统转换逻辑容易引起数值振荡,甚至错误识别节点类型而导致潮流发散。针对该问题,文中提出一种非线性规划模型以改进PV-PQ节点类型转换逻辑,采用现代内点算法求解。模型以无功容量作为约束条件,通过目标函数控制系统电压,避开了节点类型转换。同时,无功的优化配置可以增强维持系统电压的能力,增大无功裕度;结合现代内点法求解,模型表现出了处理大规模和重负荷系统的优良性能。对IEEE-118系统和一个实际系统的仿真验证了该模型的优势。

A New Kernel Function Yielding the Best Known Iteration Bounds for Primal-Dual Interior-Point Algorithms

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.

Primal-dual algorithms for total variation based image restoration under Poisson noise Dedicated to Professor Lin Qun on the Occasion of his 80th Birthday

We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.

Complexity analysis of interior-point algorithm based on a new kernel function for semidefinite optimization

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.

Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.

A variational formulation for physical noised image segmentation

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.

Three-Phase Optimal Power Flow for Study of PV Plant Distributed Impact on Distribution Systems

This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The reduction of unbalance voltage and losses in the distribution systems is obtained by actions of reactive power control of the inverter. The TOPF is formulated by current balance equations and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems for different scenarios of solar irradiance and temperature, thus providing a detailed view of the impact of photovoltaic distributed generation.

A FIRST-ORDER SPLITTING METHOD FOR SOLVING A LARGE-SCALE COMPOSITE CONVEX OPTIMIZATION PROBLEM

In this paper, we construct several efficient first-order splitting algorithms for solving a multi-block composite convex optimization problem. The objective function includes a smooth function with a Lipschitz continuous gradient, a proximable convex function that may be nonsmooth, and a finite sum composed of a proximable function and a bounded linear operator. To solve such an optimization problem, we transform it into the sum of three convex functions by defining an appropriate inner product space. Based on the dual forward-backward splitting algorithm and the primal-dual forward-backward splitting algorithm, we develop several iterative algorithms that involve only computing the gradient of the differentiable function and proximity operators of related convex functions. These iterative algorithms are matrix-inversion-free and completely splitting algorithms. Finally, we employ the proposed iterative algorithms to solve a regularized general prior image constrained compressed sensing model that is derived from computed tomography image reconstruction. Numerical results show that the proposed iterative algorithms outperform the compared algorithms including the alternating direction method of multipliers, the splitting primal-dual proximity algorithm, and the preconditioned splitting primal-dual proximity algorithm.

A New Class of Infeasible InteriorPoint Algorithm for Linear Complementarity Problem

This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log（n /ε））iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.

A Modified and Simplified Full Nesterov–Todd Step O(N)Infeasible Interior-Point Method for Second-Order Cone Optimization

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.

REDUCED BASIS METHOD FOR PARAMETRIZED ELLIPTIC ADVECTION-REACTION PROBLEMS

In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the ＂primal- dual＂ formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the ＂primal-dual＂ Reduced Basis approach with respect to an ＂only primal＂ one. Parametrized advection-reaction partial differential equations, Reduced Basis method, ＂primal-dual＂ reduced basis approach, Stabilized finite element method, a posteriori error estimation.

半定规划的近似中心投影法

Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos’s projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14].

基于运行风险的电力系统预防-校正协调控制策略

将运行风险应用于预防控制与校正控制之间的协调问题中,提出一种新的控制策略.首先,利用二层规划理论建立预防控制和校正控制的二层优化模型;然后,采用一种将内点法嵌入粒子群算法的混合解法进行该二层优化模型的求解;最后,利用6节点系统进行所提出模型与传统模型的对比性仿真.仿真计算结果表明,所提出控制策略在经济效益和运行风险方面的综合性能优于传统的安全约束调度方法,从而验证了所提出策略的合理性.