Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function

In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.

Mesoscale Wind Farm Placement via Linear Optimization Constrained by Power System and Techno-economics

The objective of this study is to develop a wind farm placement and investment methodology based on a linear optimization procedure.This problem has a major significance for the investment success for the projects of renewable energy such as wind power.In this study,a mesoscale approach is adopted whereby the wind farm location is investigated in comparison with a microscale approach where the location of each individual turbine is optimized.Specifical study focuses on the placement of a wind farm by economical optimization constrained by the power system,wind resources,and techno-economics.Linear optimization is introduced in this context at the power system which is constrained by wind farm planning.

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.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS：I．ALGORITHM AND GLOBAL CONVERGENCE

A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ．LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

Optimization of a Route Network in Dakar Airspace: Surface Navigation

In this paper, the map of a network of air routes was updated by removing the non-optimal routes and replacing them with the best ones. An integer linear programming model was developed. The aim was to find optimal routes in superspace based on performance-based navigation. The optimal routes were found from a DIJKSTRA algorithm that calculates the shortest path in a graph. Simulations with python language on real traffic areas showed the improvements brought by surface navigation. In this work, the conceptual phase and the upper airspace were studied.

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.

HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS

In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

Novel Block Chain Technique for Data Privacy and Access Anonymity in Smart Healthcare

The Internet of Things (IoT) and Cloud computing are gaining popularity due to their numerous advantages, including the efficient utilization of internetand computing resources. In recent years, many more IoT applications have beenextensively used. For instance, Healthcare applications execute computations utilizing the user’s private data stored on cloud servers. However, the main obstaclesfaced by the extensive acceptance and usage of these emerging technologies aresecurity and privacy. Moreover, many healthcare data management system applications have emerged, offering solutions for distinct circumstances. But still, theexisting system has issues with specific security issues, privacy-preserving rate,information loss, etc. Hence, the overall system performance is reduced significantly. A unique blockchain-based technique is proposed to improve anonymityin terms of data access and data privacy to overcome the above-mentioned issues.Initially, the registration phase is done for the device and the user. After that, theGeo-Location and IP Address values collected during registration are convertedinto Hash values using Adler 32 hashing algorithm, and the private and publickeys are generated using the key generation centre. Then the authentication is performed through login. The user then submits a request to the blockchain server,which redirects the request to the associated IoT device in order to obtain thesensed IoT data. The detected data is anonymized in the device and stored inthe cloud server using the Linear Scaling based Rider Optimization algorithmwith integrated KL Anonymity (LSR-KLA) approach. After that, the Time-stamp-based Public and Private Key Schnorr Signature (TSPP-SS) mechanismis used to permit the authorized user to access the data, and the blockchain servertracks the entire transaction. The experimental findings showed that the proposedLSR-KLA and TSPP-SS technique provides better performance in terms of higherprivacy-preserving rate, lower information loss, execution time, and Central Processing Unit (CPU) usage than the existing techniques. Thus, the proposed method allows for better data privacy in the smart healthcare network.

Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.

Polynomial-time interior-point algorithm based on a local self-concordant finite barrier function

The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex optimization problems. The parameters of a self-concordant barrier function can be used to compute the complexity bound of the proposed algorithm. In this paper, it is proved that the finite barrier function is a local self-concordant barrier function. By deriving the local values of parameters of this barrier function, the desired complexity bound of an interior-point algorithm based on this local self-concordant function for linear optimization problem is obtained. The bound matches the best known bound for small-update methods.

The Influence of Chemical Element on Properties of Deformed Steel Bar

In this paper, the relationship between steel and chemical elements is explored. A production record of a steel mill is adopted for two years, which is used as the basic data to standardize the data. Then, according to the correlation coefficient method between the hot-rolled ribs No. 1 and No. 2 hot-rolled ribs, the correlation between the two sets of data is analyzed. The main influencing factors of the hot-rolled ribs properties are obtained qualitatively. Then, the logistic regression method is used. Finally, according to the national standard of Chinese steel, the linear optimization model of Cr and Mn and V elements was established, and the change range of Cr was obtained without affecting the performance of hot rolled ribs.

Supply-based optimal scheduling of oil product pipelines

Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

Improved Speech Denoising Algorithm Based on Discrete Fractional Fourier Transform

The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.

The principle of optimization of binary mobile phase composition of multi-step linear gradient elution

The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with simultaneously considering effects of position of solute inside the column and mobile phase composition on peak resolution and retention value, then a BASIC program based on this principle is developed in IBM-PC computer. The validities of both principle of optimization and BASIC program are confirmed by separation of samples Containing bile acids and PAHs in RP-HPLC.

Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function

A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.