This paper presents a new neural network for solving quadratic programming problems. The new model has a simple form, furthermore it has a good convergence rate with a less number calculation operation than the old mo...
详细信息
This paper presents a new neural network for solving quadratic programming problems. The new model has a simple form, furthermore it has a good convergence rate with a less number calculation operation than the old models. It converges very fast to exact solution of the dual problem and by substituting in a formulation, the optimal solution of the original problem is obtained. Neural network model with one of numerical method is solved. Finally, simple numerical examples are provided for more illustration. (C) 2010 Elsevier Inc. All rights reserved.
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the gradient projection conjugate gradient (GPCG) algorithm for bound-cons...
详细信息
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the gradient projection conjugate gradient (GPCG) algorithm for bound-constrained convex quadratic programming [J. J. More and G. Toraldo, SIAM T. Optim., 1 (1991), pp. 93-113], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations until either a candidate active set is identified or no reasonable progress is made, and an unconstrained minimization phase, which reduces the objective function in a suitable space defined by the identification phase, by applying either the conjugate gradient method or a recently proposed spectral gradient method. However, the algorithm differs from GPCG not only because it deals with a more general class of problems, but mainly for the way it stops the minimization phase. This is based on a comparison between a measure of optimality in the reduced space and a measure of bindingness of the variables that are on the bounds, defined by extending the concept of proportional iterate, which was proposed by some authors for box-constrained problems. If the objective function is bounded, the algorithm converges to a stationary point thanks to a suitable application of the gradient projection method in the identification phase. For strictly convex problems, the algorithm converges to the optimal solution in a finite number of steps even in the case of degeneracy. Extensive numerical experiments show the effectiveness of the proposed approach.
Sports intelligence receives constant attention, especially with the development of information technology. Existing tennis-launching machines, a kind of device launching tennis balls from a fixed point, have shortcom...
详细信息
Sports intelligence receives constant attention, especially with the development of information technology. Existing tennis-launching machines, a kind of device launching tennis balls from a fixed point, have shortcomings such as limited launching height and low control accuracy, which are lack of considerable flexibility when applied in a practical situation. In this article, a tennis-training robot based on a redundant manipulator cooperated with a tennis-launching structure is presented to realize a high-precision and flexible ball-launching task. In order to construct a control scheme of the robotic system, the physical situation of tennis launching is modeled, and further transformed into a quadratic programming problem. Then, a recurrent neural network (RNN) is built to obtain the optimal solution. Furthermore, simulative experiments based on the CoppeliaSim platform using a FRANKA EMIKA manipulator are carried out to demonstrate the realizability of the designed application scenarios.
We consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications a...
详细信息
We consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications and the problem is known to be MAX SNP hard. We show that if the rank of an associated m x n cost matrix Q = (q(ij)) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank one, we provide an O(n log n) algorithm and this complexity reduces to O(n) with additional assumptions. Further, if q(ij) = a(i) + b(j) for some a(i) and b(j), then BQP01 is shown to be solvable in O(mn log n) time. By restricting m = O(log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m = O(k root n) for a fixed k. Finally, if the minimum number of rows and columns to be deleted from Q to make the remaining matrix non-negative is O(log n), then we show that BQP01 is polynomially solvable but it is NP-hard if this number is O(k root n) for any fixed k. (C) 2015 Elsevier B.V. All rights reserved.
This paper develops and demonstrates a generalized procedure for programming a quadratic function to achieve optimum performance. The method is a generalization of linear programming techniques which have been used su...
详细信息
Many scientific research and engineering problems can be converted to time-varying quadratic programming (TVQP) problems with constraints. Thus, TVQP problem solving plays an important role in practical applications. ...
详细信息
Many scientific research and engineering problems can be converted to time-varying quadratic programming (TVQP) problems with constraints. Thus, TVQP problem solving plays an important role in practical applications. Many existing neural networks, such as the gradient neural network (GNN) or zeroing neural network (ZNN), were designed to solve TVQP problems, but the convergent rate is limited. The recent varying-parameter convergent-differential neural network (VP-CDNN) can accelerate the convergent rate, but it can only solve the equality-constrained problem. To remedy this deficiency, a novel barrier varying-parameter dynamic learning network (BVDLN) is proposed and designed, which can solve the equality-, inequality-, and bound-constrained problem. Specifically, the constrained TVQP problem is first converted into a matrix equation. Second, based on the modified Karush-Kuhn-Tucker (KKT) conditions and varying-parameter neural dynamic design method, the BVDLN model is conducted. The superiorities of the proposed BVDLN model can solve multiple-constrained TVQP problems, and the convergent rate can achieve superexponentially convergence. Comparative simulative experiments verify that the proposed BVDLN is more effective and more accurate. Finally, the proposed BVDLN is applied to solve a robot motion planning problems, which verifies the applicability of the proposed model.
This paper discusses optimization problems with nonlinear inequality constraints and presents a new sequential quadratically-constrained quadratic programming (NSQCQP) method of feasible directions for solving such pr...
详细信息
This paper discusses optimization problems with nonlinear inequality constraints and presents a new sequential quadratically-constrained quadratic programming (NSQCQP) method of feasible directions for solving such problems. At each iteration. the NSQCQP method solves only one subproblem which consists of a convex quadratic objective function, convex quadratic equality constraints, as well as a perturbation variable and yields a feasible direction of descent (improved direction). The following results on the NSQCQP are obtained: the subproblem solved at each iteration is feasible and solvable: the NSQCQP is globally convergent under the Mangasarian-Fromovitz constraint qualification (MFCQ);the improved direction can avoid the Maratos effect without the assumption of strict complementarity;the NSQCQP is superlinearly and quasiquadratically convergent under some weak assumptions without thestrict complementarity assumption and the linear independence constraint qualification (LICQ).
We consider a quadratic program with a few negative eigenvalues (QP-r-NE) subject to linear and convex quadratic constraints that covers many applications and is known to be NP-hard even with one negative eigenvalue (...
详细信息
We consider a quadratic program with a few negative eigenvalues (QP-r-NE) subject to linear and convex quadratic constraints that covers many applications and is known to be NP-hard even with one negative eigenvalue (QP1NE). In this paper, we first introduce a new global algorithm (ADMBB), which integrates several simple optimization techniques such as alternative direction method, and branch-and-bound, to find a globally optimal solution to the underlying QP within a pre-specified epsilon-tolerance. We establish the convergence of the ADMBB algorithm and estimate its complexity. Second, we develop a global search algorithm (GSA) for QP1NE that can locate an optimal solution to QP1NE within epsilon-tolerance and estimate the worst-case complexity bound of the GSA. Preliminary numerical results demonstrate that the ADMBB algorithm can effectively find a global optimal solution to large-scale QP-r-NE instances when r <= 10, and the GSA outperforms the ADMBB for most of the tested QP1NE instances.
The presence of multiple constraints due to network line flow limits and emission allowances in economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. Thi...
详细信息
The presence of multiple constraints due to network line flow limits and emission allowances in economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. This paper proposes a practical strategy based on quadratic programming (QP) techniques to solve the real-time economic dispatch problem. It formulates the problem with a quadratic objective function based on the unit's cost curves in quadratic or piecewise-quadratic forms. The operation constraints are modeled as linear equality/inequality equations, resulting in a typical QP problem. Goal programming techniques are also incorporated in the formulation which guarantees the best available solution even under infeasible conditions. In addition, the proposed strategy formulates the problem in the second phase dispatch in real time by including a set of emergency control variables to provide effective control strategies for properly relieving constraint violations if they exist. The effectiveness of the proposed strategy is demonstrated by an example power dispatch problem.
quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the l...
详细信息
quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons & Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications. (C) 2008 Elsevier Ltd. All rights reserved.
暂无评论