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.

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 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.

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.

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.

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.

Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs

When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

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.

Checking weak and strong optimality of the solution to interval convex quadratic program

In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.

Automatic differentiation for reduced sequential quadratic programming

In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.

AN INEXACT LAGRANGE-NEWTON METHOD FOR STOCHASTIC QUADRATIC PROGRAMS WITH RECOURSE

In this paper,two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular,the convergence is local superlinear under an integral approximation error bound condition.Moreover,this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.

A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF MAX-BISECTION

A successive quadratic programming algorithm for solving SDP relaxation of Max- Bisection is provided and its convergence result is given. The step-size in the algorithm is obtained by solving n easy quadratic equations without using the linear search technique. The numerical experiments show that this algorithm is rather faster than the interior-point method.

Stability analysis of proportional delayed projection neural network for quadratic programming problem

At present,projection neural network(PNN)with bounded time delay has been widely used for solving convex quadratic programming problem(QPP).However,there is little research concerning PNN with unbounded time delay.In this paper,we propose the proportional delayed PNN to solve QPP with equality constraints.By utilizing homeo morphism mapping principle,we prove the proportional delayed PNN exists with unique equilibrium point which is the optimal solution of QPP.Simultaneously,delay-dependent criteria about global exponential stability(GES)and global polynomial stability(GPS)are also acquired by applying the method of variation of constants and inequality techniques.On the other hand,when proportional delay factor q is equal to 1,the proportional delayed PNN becomes the one without time delay which still can be utilized for solving QPP.But in most situations,q is not equal to 1,and time delay is unpredictable and may be unbounded in the actual neural network,which causes instability of system.Therefore,it is necessary to consider proportional delayed PNN.A numerical example demonstrates that,compared with the proportional delayed Lagrange neural network,the proportional delayed PNN is faster in terms of convergence rate.The possible reason is that appropriate parameters make the model converge to the equilibrium point along the direction of gradient descent.

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.

Sequential quadratic programming particle swarm optimization for wind power system operations considering emissions

In this paper,a computation framework for addressing combined economic and emission dispatch(CEED)problem with valve-point effects as well as stochastic wind power considering unit commitment(UC)using a hybrid approach connecting sequential quadratic programming(SQP)and particle swarm optimization(PSO)is proposed.The CEED problem aims to minimize the scheduling cost and greenhouse gases(GHGs)emission cost.Here the GHGs include carbon dioxide(CO_(2)),nitrogen dioxide(NO_(2)),and sulphur oxides(SO_(x)).A dispatch model including both thermal generators and wind farms is developed.The probability of stochastic wind power based on the Weibull distribution is included in the CEED model.The model is tested on a standard system involving six thermal units and two wind farms.A set of numerical case studies are reported.The performance of the hybrid computational method is validated by comparing with other solvers on the test system.

Subspace Search Method for Quadratic Programming With BoxConstraints

A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.

Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems

In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.

Smooth free-cycle dynamic soaring in unspecified shear wind via quadratic programming

Harvesting wind energy is promising for extending long-endurance flights,which can be greatly facilitated by a flight technique called dynamic soaring.The presented study is concerned with generating model-based trajectories with smooth control histories for dynamic soaring maneuvers exploiting wind gradients.The desired smoothness is achieved by introducing a trigonometric series parameterization for the controls,which are formulated with respect to the normalized time.Specifically,the periodicity of the trigonometric functions is leveraged to facilitate the connection of cycles and streamline the problem formulation.Without relying on a specified wind profile,a freefinal-time quadratic programming-based control strategy is developed for the online correction of the flight trajectory,which requires only the instant wind information.Offline and online numerical studies show the trade-off to achieve the smoothness and demonstrate the effectiveness of the proposed method in a varying wind field.