A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.

A predictor-corrector interior-point algorithmfor monotone variational inequality problems

Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

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.

Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming

In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size.

Power System Reactive Power Optimization Based on Fuzzy Formulation and Interior Point Filter Algorithm

Considering the soft constraint characteristics of voltage constraints, the Interior-Point Filter Algorithm is applied to solve the formulation of fuzzy model for the power system reactive power optimization with a large number of equality and inequality constraints. Based on the primal-dual interior-point algorithm, the algorithm maintains an updating “filter” at each iteration in order to decide whether to admit correction of iteration point which can avoid effectively oscillation due to the conflict between the decrease of objective function and the satisfaction of constraints and ensure the global convergence. Moreover, the “filter” improves computational efficiency because it filters the unnecessary iteration points. The calculation results of a practical power system indicate that the algorithm can effectively deal with the large number of inequality constraints of the fuzzy model of reactive power optimization and satisfy the requirement of online calculation which realizes to decrease the network loss and maintain specified margins of voltage.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

An Improved Affine-Scaling Interior Point Algorithm for Linear Programming

In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.

Predictor-corrector interior-point algorithm for linearly constrained convex programming

Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.

A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS

A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.

A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems

A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.

A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.

Optimal Adjustment Algorithm for <i>p</i>Coordinates and The Starting Point in Interior Point Methods

Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.

单调线性权互补问题的新全牛顿步可行内点算法

提出求解单调线性权互补问题(WLCP)的全牛顿步可行内点算法。基于线性优化的连续可微函数,给出中心方程的新等价形式,接着运用牛顿法求解定义中心路径的等价方程组,从而得到单调WLCP的新搜索方向。沿该搜索方向使用全牛顿步,无需进行线搜索。通过适当选取参数,分析了全牛顿步的严格可行性,证得算法是二次收敛的且具有多项式时间迭代复杂度。最后数值实验结果表明算法有效。

基于ADE优化的IPMSM全速域无传感器控制

为了实现内置式永磁同步电机(IPMSM)全速域的无传感器控制和切换速域的平滑过渡,提出了一种基于自适应差分进化(ADE)算法优化的复合控制方法。分别在零低速域、中高速域采用旋转高频电压注入法和滑模观测器法来对电机转速和转子位置进行估算,并在切换速域采用基于ADE算法的权重系数优化法来实现上述两种控制方法的平滑切换,从而实现IPMSM全速域无传感器控制。仿真结果表明:提出的复合控制方法能够实现电机全速域的无感控制和切换速域的平滑过渡,且具有良好的稳定性。

基于鲸鱼算法的内弹道性能优化

针对某航炮对最大炮口初速越来越高的要求,以提高最大炮口初速为优化设计目标,对弧厚和发射药药量进行优化设计。选用具有操作简单、跳出局部最优的能力强等优点的鲸鱼算法,将鲸鱼算法与该炮内弹道数学模型相结合,对内弹道性能进行优化。结果表明:该方法优化效果较好,最大炮口初速得到了有效提升,所采用的鲸鱼算法与内弹道相结合是可行的,为后续其他类型火炮内弹道设计提供了一定参考。

双极板设备用内置式永磁同步电机结构优化

为了有效地提高永磁同步电机的转矩性能和降低齿槽转矩,选取48槽、8极的内置式永磁同步电机为例,在不改变转子径向半径的前提下,选取转子的关键参数作为优化参数,基于田口算法对内置式永磁同步电机进行多目标优化,在有效降低齿槽转矩的基础上增大内置式永磁同步电机的转矩性能。在优化基础上,对空载运行、额定负载、最高转速3种永磁同步电机典型的运转工况进行有限元仿真。数据结果表明:齿槽转矩峰峰值从1.8 N·m降低至0.9 N·m,额定负载下的平均电磁转矩从73.17 N·m增长至77.12 N·m,最高转速运行下的平均电磁转矩从37.3 N·m增长值38.42 N·m,分别实现了提高永磁同步电机转矩性能和降低齿槽转矩的目标。

求解双层规划问题的松弛序列二次规划方法

考虑一类具有特殊结构的双层规划问题,其下层问题为凸问题.首先通过内点罚方法将下层的约束函数惩罚到目标函数,使得下层问题近似为一系列无约束优化问题.然后使用KKT条件替换无约束的下层问题的最优解集,那么双层规划问题被一系列松弛的单层问题近似.文中设计了一种光滑的序列二次规划算法求解该松弛问题,并证明了当罚因子趋近于0时,该算法生成的迭代点列收敛到双层规划问题的弱稳定点.数值实验验证了算法的可行性.

Fast Distributed Demand Response Algorithm in Smart Grid

This paper proposes a fast distributed demand response U+0028 DR U+0029 algorithm for future smart grid based on primaldual interior method and Gaussian belief propagation U+0028 GaBP U+0029 solver. At the beginning of each time slot, each end-user U+002F energysupplier exchanges limited rounds of messages that are not private with its neighbors, and computes the amount of energy consumption U+002F generation locally. The proposed demand response algorithm converges rapidly to a consumption U+002F generation decision that yields the optimal social welfare when the demands of endusers are low. When the demands are high, each end-user U+002F energysupplier estimates its energy consumption U+002F generation quickly such that a sub-optimal social welfare is achieved and the power system is ensured to operate within its capacity constraints. The impact of distributed computation errors on the proposed algorithm is analyzed theoretically. The simulation results show a good performance of the proposed algorithm. © 2017 Chinese Association of Automation.

Numerical simulation and optimized design of cased telescoped ammunition interior ballistic

In order to achieve the optimized design of a cased telescoped ammunition(CTA) interior ballistic design,a genetic algorithm was introduced into the optimal design of CTA interior ballistics with coupling the CTA interior ballistic model. Aiming at the interior ballistic characteristics of a CTA gun, the goal of CTA interior ballistic design is to obtain a projectile velocity as large as possible. The optimal design of CTA interior ballistic is carried out using a genetic algorithm by setting peak pressure, changing the chamber volume and gun powder charge density. A numerical simulation of interior ballistics based on a 35 mm CTA firing experimental scheme was conducted and then the genetic algorithm was used for numerical optimization. The projectile muzzle velocity of the optimized scheme is increased from 1168 m/s for the initial experimental scheme to 1182 m/s. Then four optimization schemes were obtained with several independent optimization processes. The schemes were compared with each other and the difference between these schemes is small. The peak pressure and muzzle velocity of these schemes are almost the same. The result shows that the genetic algorithm is effective in the optimal design of the CTA interior ballistics. This work will be lay the foundation for further CTA interior ballistic design.