Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

A novel image segmentation approach for wood plate surface defect classification through convex optimization

Detection of wood plate surface defects using image processing is a complicated problem in the forest industry as the image of the wood surface contains different kinds of defects. In order to obtain complete defect images, we used convex optimization(CO) with different weights as a pretreatment method for smoothing and the Otsu segmentation method to obtain the target defect area images. Structural similarity(SSIM) results between original image and defect image were calculated to evaluate the performance of segmentation with different convex optimization weights. The geometric and intensity features of defects were extracted before constructing a classification and regression tree(CART) classifier. The average accuracy of the classifier is 94.1% with four types of defects on Xylosma congestum wood plate surface: pinhole, crack,live knot and dead knot. Experimental results showed that CO can save the edge of target defects maximally, SSIM can select the appropriate weight for CO, and the CART classifier appears to have the advantages of good adaptability and high classification accuracy.

Learning Convex Optimization Models

A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.

Performance Analysis of Sparse Array based Massive MIMO via Joint Convex Optimization

Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective implementation of massive MIMO challenging,due to the size and weight limits of the masssive MIMO that are located on each BS.Therefore,in order to miniaturize the massive MIMO,it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis.In this paper,a multiple-pattern synthesis is considered towards convex optimization(CO).The joint convex optimization(JCO)based synthesis is proposed to construct a codebook for beamforming.Then,a criterion containing multiple constraints is developed,in which the sparse array is required to fullfill all constraints.Finally,extensive evaluations are performed under realistic simulation settings.The results show that with the same number of antenna elements,sparse array using the proposed JCO-based synthesis outperforms not only the uniform array,but also the sparse array with the existing CO-based synthesis method.Furthermore,with a half of the number of antenna elements that on the uniform array,the performance of the JCO-based sparse array approaches to that of the uniform array.

Computation of Peak Output for Inputs Restricted in L_2 and L_∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization

In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

The Application of Convex Optimization to Load Optimal Allocation in a Single Workstation System

The service quality of a workstation depends mainly on its service load, ifnot taking into account all kinds of devices' break-downs. In this article, an optimization modelwith inequality constraints is proposed, which aims to minimize the service load. A noveltransformation of optimization variables is also devised and the constraints are properly combinedso as to make this model into a convex one, whose corresponding Lagrange function and the KKTconditions are established afterwards. The interior-point method for convex optimization ispresented here as an efficient computation tool. Finally, this model is evaluated by a real example,from which conclusions are reached that the interior-point method possesses advantages such asfaster convergeoce and fewer iterations and it is possible to make complicated nonlinearoptimization problems exhibit convexity so as to obtain the optimum.

Application of Convex Optimization to Queuing Systems

On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.

Convex Optimization-Based Rotation Parameter Estimation Using Micro-Doppler

We present a novel algorithm that can determine rotation-related parameters of a target using FMCW （frequency modulated continuous wave） radars, not utilizing inertia information of the target. More specifically, the proposed algorithm estimates the angular velocity vector of a target as a function of time, as well as the distances of scattering points in the wing tip from the rotation axis, just by analyzing Doppler spectrograms obtained from three or more radars. The obtained parameter values will be useful to classify targets such as hostile warheads or missiles for real-time operation, or to analyze the trajectory of targets under test for the instrumentation radar operation. The proposed algorithm is based on the convex optimization to obtain the rotation-related parameters. The performance of the proposed algorithm is assessed through Monte Carlo simulations. Estimation performance of the proposed algorithm depends on the target and radar geometry and improves as the number of iterations of the convex optimization steps increases.

Research on Optimizing Computer Network Structure based on Genetic Algorithm and Modified Convex Optimization Theory

In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in the background and one of its core problems is to solve the optimization problem. Unlike traditional batch algorithm, stochastic gradient descent algorithm in each iteration calculation, the optimization of a single sample point only losses could greatly reduce the memory overhead. The experiment illustrates the feasibility of our proposed approach.

A Regularized Newton Method with Correction for Unconstrained Convex Optimization

In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.

Multiconstraint adaptive three-dimensional guidance law using convex optimization

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.

Cooperative User-Scheduling and Resource Allocation Optimization for Intelligent Reflecting Surface Enhanced LEO Satellite Communication

Lower Earth Orbit(LEO) satellite becomes an important part of complementing terrestrial communication due to its lower orbital altitude and smaller propagation delay than Geostationary satellite. However, the LEO satellite communication system cannot meet the requirements of users when the satellite-terrestrial link is blocked by obstacles. To solve this problem, we introduce Intelligent reflect surface(IRS) for improving the achievable rate of terrestrial users in LEO satellite communication. We investigated joint IRS scheduling, user scheduling, power and bandwidth allocation(JIRPB) optimization algorithm for improving LEO satellite system throughput.The optimization problem of joint user scheduling and resource allocation is formulated as a non-convex optimization problem. To cope with this problem, the nonconvex optimization problem is divided into resource allocation optimization sub-problem and scheduling optimization sub-problem firstly. Second, we optimize the resource allocation sub-problem via alternating direction multiplier method(ADMM) and scheduling sub-problem via Lagrangian dual method repeatedly.Third, we prove that the proposed resource allocation algorithm based ADMM approaches sublinear convergence theoretically. Finally, we demonstrate that the proposed JIRPB optimization algorithm improves the LEO satellite communication system throughput.

Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations and Compressive Affine Phase Retrieval

Separable multi-block convex optimization problem appears in many mathematical and engineering fields.In the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem,and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices.Affine phase retrieval arises in holography,data separation and phaseless sampling,and it is also considered as a nonhomogeneous version of phase retrieval,which has received considerable attention in recent years.Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval,in the second part of this paper,we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization,and then based on the proposed inertial proximal ADMM for 3-block convex optimization,we propose an algorithm to recover sparse real signals from their(noisy)affine quadratic measurements.Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.

Boosting for Distributed Online Convex Optimization

Decentralized Online Learning(DOL)extends online learning to the domain of distributed networks.However,limitations of local data in decentralized settings lead to a decrease in the accuracy of decisions or models compared to centralized methods.Considering the increasing requirement to achieve a high-precision model or decision with distributed data resources in a network,applying ensemble methods is attempted to achieve a superior model or decision with only transferring gradients or models.A new boosting method,namely Boosting for Distributed Online Convex Optimization(BD-OCO),is designed to realize the application of boosting in distributed scenarios.BD-OCO achieves the regret upper bound O(M+N/MNT)where M measures the size of the distributed network and N is the number of Weak Learners(WLs)in each node.The core idea of BD-OCO is to apply the local model to train a strong global one.BD-OCO is evaluated on the basis of eight different real-world datasets.Numerical results show that BD-OCO achieves excellent performance in accuracy and convergence,and is robust to the size of the distributed network.

First-Order Algorithms for Convex Optimization with Nonseparable Objective and Coupled Constraints

In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propose a number of first-order algorithms to solve this model.First,the alternating direction method of multipliers(ADMM)is extended,assuming that it is easy to optimize the augmented Lagrangian function with one block of variables at each time while fixing the other block.We prove that O(1/t)iteration complexity bound holds under suitable conditions,where t is the number of iterations.If the subroutines of the ADMM cannot be implemented,then we propose new alternative algorithms to be called alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof.Under suitable conditions,the O(1/t)iteration complexity bound is shown to hold for all the newly proposed algorithms.Finally,we extend the analysis for the ADMM to the general multi-block case.

Survey of convex optimization for aerospace applications

Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

Convex optimization of asteroid landing trajectories driven by solar radiation pressure

High-area/mass ratio landers driven by Solar Radiation Pressure(SRP)have potential applications for future asteroid landing missions.This paper develops a new convex optimization-based method for planning trajectories driven by SRP.A Minimum Landing Error(MLE)control problem is formulated to enable planning SRP-controlled trajectories with different flight times.It is transformed into Second Order Cone Programming(SOCP)successfully by a series of different convexification technologies.A trust region constraint and a modified MLE objective function are used to guarantee the convergence performance of the optimization algorithm.Thereafter,the SRP-driven trajectory optimal control problem is converted equivalently into a sequence of convex optimal control problems that can be solved effectively.A set of numerical simulation results has verified the effectiveness and feasibility of the proposed optimization method.

Stable and Total Fenchel Duality for Composed Convex Optimization Problems

In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.