Unconstrained Optimization Model Research Articles

Wideband MIMO Radar Waveform Design for Multiple Target Imaging

This paper focuses on the design of wideband multiple-input multiple-output (MIMO) radar waveform and its application to multi-target imaging. In a multiple targets scenario, the imaging performances are affected by the transmit beampattern and the power spectral density (PSD) illuminating on targets. Taking into account these factors, we have established an unconstrained optimization model based on jointly minimizing the matching errors of the beampattern and PSDs. To solve the large-scale optimization problem, a conjugate gradient-based wideband MIMO waveform design method is proposed. For the purpose of improving the computational efficiency, the Chirp-Z transform is employed in evaluating the discrete frequency spectrum. Numerical results show that the proposed method can approximately realize the desired multibeam and PSDs. By utilizing a sparse representation method, the designed waveform with randomly distributed PSDs can be applied to multi-target imaging.

On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems

In this paper, we study a new exact and smooth penalty function for the nonlinear mixed discrete programming problem by augumenting only one variable no matter how many constraints. Through the smooth and exact penalty function, we can transform the nonlinear mixed discrete programming problem into an unconstrained optimization model. We demonstrate that under mild conditions, when the penalty parameter is sufficiently large, optimizers of this penalty function are precisely the optimizers of the nonlinear mixed discrete programming problem. Alternatively, under some mild assumptions, the local exactness property is also presented. The numerical results demonstrate that the new penalty function is an effective and promising approach. As important applications, we solve an increasingly popular search engine advertising problem via the new proposed penalty function.

AN IMPROVED PROJECTION ONTO CONVEX SETS METHOD FOR SIMULTANEOUS INTERPOLATION AND DENOISING

AbstractSparsity‐promoted seismic interpolation is an important interpolation strategy; however, most existing interpolation methods merely focused on high signal‐to‐noise ratio data. Actually, noise is always contained in sampled data; the existence of noise will deteriorate interpolation results and makes interpolation challenging. Projection onto convex sets (POCS) method is an efficient method; however, it cannot get acceptable results for noisy data interpolation. A strategy for simultaneous interpolation and denoising is the weighted POCS method which uses an additional weighting factor to achieve denoising. In this paper, we demonstrate that the weighted projection onto convex sets (POCS) method is a method for unconstrained optimization model, and it can be deduced from the iterative thresholding method. In addition, an improved POCS method is proposed for interpolation and denoising without extra computation effort. Numerical examples on synthetic and field data demonstrate that the improved POCS method can get reliable results for noiseless and noisy data interpolation. First interpolation and then denoising examples proved that simultaneous interpolation and denoising is robust when the least thresholds are properly chosen.

An Intelligent Household Electricity Load Control Method Based on Demand Response

This paper presents a method for smart house electricity load control. The method, combined with TOU price and Real-time pricing, arranges various appliances and meets daily household electricity demand at the same time, so that to reduce the daily electricity consumption and realize Demand Response. First, this paper attempts to summarize problem witch need to be solved for realizing load control in a smart house. Second, the smart house load control problem was described as high-dimensional complex functions unconstrained optimization model and solved with Particle Swarm Optimization. Finally, design experiments used the method for a smart house. Experimental results show that the method can arrange various appliances and reduce electricity consumption.

A convex optimization-based traffic matrix estimation approach in IP-over-WDM backbone networks

With the rapid development of an IP-over-WDM network, it has become a complex and heterogeneous network. In such a case, network management is a crucial role for promoting the efficiency of the IP-over-WDM network. A traffic matrix, which provides an intrinsic and flow-level view of our networks, is required to perform network management tasks such as traffic engineering function. Unfortunately, limited by current technologies, it is significantly difficult to acquire the exact traffic matrix. Motivated by this issue, in this paper, we investigate the traffic matrix estimation problem in an IP-over-WDM backbone network. We develop a simple algorithm based on the network tomography method. In order to deal with the ill-posed property of the traditional network tomography method, we refer to the origin–destination traffic demands of the optical layer in our method. We first study the relationship between the traffic matrix and optical layer traffic demands. Thereby, we take advantage of the relationship between them to construct a linear system. Combining with the traditional network tomography model, we propose a convex and unconstrained optimization model for estimating the traffic matrix. Finally, we also provide numerical results to validate the performance of the proposed method in this literature.

Study of Computation for Structural Reliability Index Based on Penalty Function Method

According to the geometric meaning of the structural reliability index, an unconstrained optimization model with structural reliability index and design point is obtained by exterior penalty function method. The Powell method, golden section method and extrapolation method are used to solve the unconstrained optimization problem. The proposed method not has to deal with the any derivative of the limited state function, and can been used to obtain structural reliability index and design point of the strong nonlinear limit state function, which first-order reliability method (FORM) may fail to converge. Three examples are given to compare penalty function method with the difference methods. The results show that the given method is simply, effective and precise enough.

A Modified Class of Conjugate Gradient Algorithms Based on Quadratic Model for Nonlinear Unconstrained Optimization

In this paper, we have investigated a new class of conjugate gradient algorithms for unconstrained non-linear optimization which are based on the quadratic model. Some theoretical results are investigated which are sufficient descent and ensure the local convergence of the new proposed algorithms. Numerical results show that the proposed algorithms are effective by comparing with the Polak and Ribiere algorithm.

Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization

We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.

Complex Differential Evolution Algorithm for Inverse Kinematics of Spatial 6R Robot Manipulators

A 6-DOF Stautli industrial robot manipulator of TX60 type is regarded as the research object, and then nonlinear equations are constructed to solve its inverse positional problems by means of kinematics analysis. Taking the minimizing pose error of the end-effector as the objective function, this study transforms the nonlinear equations into an unconstrained optimization model and employs a differential evolution(DE) algorithm to solve this problem. To overcome the defects of the simple DE algorithm that is difficult to keep balance between the convergence accuracy and the calculation reliability, an adaptive division complex DE(ADCDE) algorithm is presented to enhance its optimizing performance. This proposed algorithm divides adaptively the population into exploitation and exploration subgroups, furthermore, the former and latter apply the DE/best/2/bin strategy and the complex operator to generate mutation individuals, respectively. With a study case for engineering application, the ADCDE algorithm is implemented to find the inverse positional solutions of a serial robot manipulator. Simulation results indicate that the presented algorithm outperforms the compared algorithms in term of computational precision and reliability, and the inverse solutions with high precision and all possible ones can be obtained by this algorithm with light calculation cost. Moreover, these results also verify the effectiveness and feasibility of this approach.

A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization

We propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

Subspace trust-region algorithm with conic model for unconstrained optimization

In this paper, a new subspace algorithm is proposed for unconstrained optimization. In this new algorithm, the subspace technique is used in the trust region subproblem with conic model, and the dogleg method is modified to solve this subproblem. The global convergence of this algorithm under some reasonable conditions is established. Numerical experiment shows that this algorithm may be superior to the corresponding algorithm without using subspace technique especially for large scale problems.

A New Smooth Support Vector Machine Based on a Rational Function

Smooth support vector machine (SSVM) is a strong convex, smooth, and unconstrained optimization model transformed from traditional support vector machine (SVM). In this study, a new smooth function which is a rational function diffrent from those polynomial functions , is used to smoothen the model of support vector machine. A new SSVM based on this rational function (Rational-SSVM) is obtained. Furthermore, Rational-SSVM is better than those SSVMs based on polynomial functions by the precision analysis.

A filter-trust-region method based on conic model for unconstrained optimization

Conic model optimization methods are one class of non-quadratic model optimization methods. It contains richer interpolation information than the standard quadratic model. Di and Sun (1996) proposed a trust-region method based on conic model for unconstrained optimization. Based on Di and Sun (1996), this paper employs the filter technique due to Fletcher and Leyffer (2002) and proposes a filter-trust-region method based on conic model for unconstrained optimization. Under mild conditions, we prove the convergence of new algorithm. Limited numerical results show that the new algorithm is efficient.

Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method

An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the minimun circumscribed circle assessment. One example is given to verify the theoretical results presented.

Mathematical Model for Evaluating Roundness Errors by Maximum Inscribed Circle Method

An unconstrained optimization model is established for assessing roundness errors by the maximum inscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the maximum inscribed circle assessment. One example is given to verify the theoretical results presented.

A Non-Monotone Trust Region Algorithm with Memory Model for Unconstrained Optimization

A Non-Monotone Trust Region Algorithm with Memory Model for Unconstrained Optimization

Mathematical Model for Evaluating Cylindricity Errors by Minimum Zone Method

An unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be applied to solve the objective function in order to get the wanted cylindricity errors by the minimun zone assessment. An example is given to verify the theoretical results presented.

Mathematical Model for Evaluating Cylindricity Errors by Maximum Inscribed Cylinder

An unconstrained optimization model applicable to radial deviation measurement is established for assessing cylindricity errors by the maximum inscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the maximum inscribed cylinder assessment. An example is given to verify the theoretical results presented.

A Novel Smooth Support Vector Regression Based on CHKS Function

This paper presents a new smooth approach to solve support vector regression (SVR). Based on Karush-Kuhn-Tucker complementary condition in optimization theory, a smooth unconstrained optimization model for SVR is built. Since the objective function of the unconstrained SVR model is non-smooth, we apply the smooth techniques and replace the ε-insensitive loss function by CHKS function. Newton-Armijo algorithm is used to solve the smooth CHKS-SSVR model. Primary numerical results illustrate that our proposed approach improves the regression performance and the learning efficiency.

Some Properties of Mathematical Model for Cylindricity Errors

An unconstrained optimization model, applicable to radial deviation measurement, is established for assessing cylindricity errors by the minimum circumscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly investigated. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the minimum circumscribed cylinder assessment. An example is given to verify the theoretical results presented.