Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method

The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.

基于SQP-GPMP2算法的移动机器人路径规划

针对高斯过程路径规划算法(GPMP2)处理非线性不等式约束能力有限、在复杂障碍物地图中易陷入局部极小值,进而产生碰撞的问题,结合序列二次规划(SQP)算法,提出了改进的SQP-GPMP2算法。首先,该算法从概率的角度将运动规划视为轨迹优化,得到初始轨迹状态;其次,引入碰撞代价函数,用来表示机器人和障碍物的碰撞代价关系;最后,使用SQP算法对轨迹进行迭代修正,保证轨迹的无碰撞和运动学合理性。仿真实验结果显示,相比GPMP2等算法,所提算法在不同尺寸迷宫上的规划成功率至少提高20个百分点,证明该算法在处理复杂约束能力和保证路径规划效率上具有优越性。

基于SQP算法的厢舱类产品快速设计技术研究

针对大规模定制背景下产品设计制造过程中遇到的轻量化和强度校核等需求,提出了一种基于序列二次规划(SQP)算法的结构优化与快速设计方法。以方舱为实例对象,按照最优控制理论构建产品关键参数设计数学计算模型,并运用SQP算法实现参数的最优求解,同时通过产品族模块化划分和参数化变型配置技术实现产品结构的快速设计。最后通过二次开发构建了相应的数字化设计平台,验证了该方法的可行性。结果表明:该方法能有效提高产品结构设计的效率和合理性。

基于GCN和QP的智能车辆换道决策规划

考虑动态驾驶场景下车辆间的交互影响,提出了一种基于图卷积网络和二次规划的智能车辆自主换道行为决策与运动规划方法.首先将感兴趣区域进行分层建模,以图结构数据的形式对驾驶场景的全局和局部动态交互信息进行聚合,通过图卷积网络输出自车应采取的驾驶行为决策指令,然后与运动规划模块结合,基于局部子图划分可通行区域,构建并求解二次规划模型,得到满足运动学约束的无碰撞运动轨迹,最终完成无碰撞自主换道.对提出的方法进行了仿真实验与实车验证,实验结果证明该方法的性能要优于传统的规划方法,具有更好的实验成功率以及场景泛化性能.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

Priority approach based on quadratic programming model to fuzzy preference relation

We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the priority vector of a fuzzy preference relation. Theprominent characteristic of the developed approach is that the priority vector can generally beobtained by a simple formula, which is derived from a quadratic programming model. We utilize theconsistency ratio to check the consistency of fuzzy preference relation. If the fuzzy preferencerelation is of unacceptable consistency, then we can return it to the decision maker to reconsiderstructuring a new fuzzy preference relation until the fuzzy preference relation with acceptableconsistency is obtained. We finally illustrate the priority approach by two numerical examples. Thenumerical results show that the developed approach is straightforward, effective, and can easily beperformed on a computer.

Design and analysis of recurrent neural network models with non-linear activation functions for solving time-varying quadratic programming problems

A special recurrent neural network(RNN),that is the zeroing neural network(ZNN),is adopted to find solutions to time-varying quadratic programming(TVQP)problems with equality and inequality constraints.Howevet,there are some weaknesses in activation functions of traditional ZNN models,including convex restriction and redundant formulation.With the aid of different activation functions,modified ZNN models are obtained to overcome the drawbacks for solving TVQP problems.Theoretical and experimental research indicate that the proposed models are better and more effective at solving such TVQP problems.

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.

Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Global optimality conditions for quadratic 0-1 programming with inequality constraints

Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.

A Quadratic Programming Model for Blast Scheduling

A quadratic programming model is established to choose the blocks to be blasted in a given period. The length of this period depends on the production planning requirements. During the given period, the blocks' parameters are available from the geological database of the mine. The objective is to minimize the deviation of the average ore grade of blasted blocks from the standard ore grade required by the mill. Transportation ability constraint. production quantity demand constraint. minimum safety bench constraint. block size constraint and block, bench precedence constraints are considered in forming the programming model. This model has more practical objective function and reasonable constraints compared with the existing model for this kind of problems.

Genetic Algorithm for Solving Quadratic Bilevel Programming Problem

By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.

MIXED ENERGY METHOD FOR SOLUTION OF QUADRATIC PROGRAMMING PROBLEMS AND ELASTIC-PLASTIC ANALYSIS OF TRUSS STRUCTURES

A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method proposed is different from the traditionalone, for which the unknown variables are selected just in one classsuch as displacements or stresses. The present method selects thevariables in the mixed form with both displacement and stress. As themethod is established in the hybrid space, the information found inthe previous incremental step can be used for the solution of thepresent step, making the algorithm highly effi- cient in thenumerical solution process of quadratic programming problems. Theresults obtained in the exm- ples of the elastic-plastic solution ofthe truss structures verify what has been predicted in thetheoretical anal- ysis.

An Interval Maximum Entropy Method for Quadratic Programming Problem

With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.

Fixed-Point Iteration Method for Solving the Convex Quadratic Programming with Mixed Constraints

The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.

A New Heuristic for the Convex Quadratic Programming Problem

This paper presents a new heuristic to linearise the convex quadratic programming problem. The usual Karush-Kuhn-Tucker conditions are used but in this case a linear objective function is also formulated from the set of linear equations and complementarity slackness conditions. An unboundedness challenge arises in the proposed formulation and this challenge is alleviated by construction of an additional constraint. The formulated linear programming problem can be solved efficiently by the available simplex or interior point algorithms. There is no restricted base entry in this new formulation. Some computational experiments were carried out and results are provided.

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.

Successive quadratic programming multiuser detector

Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefmite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

Quadratic Programming-based Approach for Autonomous Vehicle Path Planning in Space

Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades.The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one,and also can not solve the inherent constraints arising from the robot body and the exterior environment.To address these difficulties,this research aims to provide a feasible trajectory based on quadratic programming（QP） for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles.First,the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target,as well as the angle between the velocity and the position in the relative velocity coordinates（RVCs）.The optimization is in quadratic polynomial form according to QP formulation.Then,the avoidance task is modeled with linear constraints in RVCs.Some other constraints,such as kinematics,dynamics,and sensor range,are included.Last,simulations with typical multiple obstacles are carried out,including in static and dynamic environments and one of human-in-the-loop.The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances.Therefore,the QP model proposed in this paper not only adapts to dynamic environment with uncertainty,but also can satisfy all kinds of constraints,and it provides an efficient approach to solve the problems of path planning in three-dimensional space.