In this paper we give corrections to our paper on an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints.
In this paper we give corrections to our paper on an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints.
We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing re...
详细信息
We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. To deal with the parallel approximablity of these problems, we show first a parallel additive approximation procedure to a subclass of multi-valued quadratic programming, called smooth multi-valued QP, which is defined by imposing certain restrictions on the coefficients of the instance. We use this procedure to obtain parallel approximation to dense instances of the two problems by observing that dense instances of these problems are instances of smooth multi-valued QP. The dense instances of the problems considered here are defined similarly as for other combinatorial problems in the literature. For such instances we can find in parallel a near optimal schedule. The definition of smooth multi-valued QP as well as the procedure for approximating it in parallel are of interest independently of the application to the scheduling problems considered in this paper.
Two domain decomposition methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These methods are based on the FETI and FETI-DP substructuri...
详细信息
Two domain decomposition methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These methods are based on the FETI and FETI-DP substructuring algorithms. In the case of linear constraints, they do not perform any Newton-like iteration. Instead, they solve a constrained problem by an active set strategy and a generalized conjugate gradient based descent method equipped with controls to guarantee convergence monotonicity, Both methods possess the desirable feature of minimizing numerical oscillations during the iterative Solution process. Performance results and comparisons are reported for several numerical simulations that suggest that both methods are numerically scalable with respect to both the problem size and the]lumber Of subdomains. Their parallel scalability is also illustrated on a Linux cluster for a complex 1.4 million degree of freedom multibody problem with frictionless contact and nonconforming discrete interfaces. (C) 2009 Elsevier B.V. All rights reserved.
Zeroing neural network (ZNN, or termed Zhang neural network after its inventor), being a special type of neurodynamic methodology, has shown powerful abilities to solve a great variety of time-varying problems with mo...
详细信息
Zeroing neural network (ZNN, or termed Zhang neural network after its inventor), being a special type of neurodynamic methodology, has shown powerful abilities to solve a great variety of time-varying problems with monotonically increasing odd activation functions. However, the existing results on ZNN cannot handle the inequality constraint in the optimization problem and nonconvex function cannot applied to accelerating the convergence speed of ZNN. This work breaks these limitations by proposing ZNN models, allowing nonconvex sets for projection operations in activation functions and incorporating new techniques for handing inequality constraint arising in optimizations. Theoretical analyses reveal that the proposed ZNN models are of global stability with timely convergence. Finally, illustrative simulation examples are provided and analyzed to substantiate the efficacy and superiority of the proposed ZNN models for real-time dynamic quadratic programming subject to equality and inequality constraints. (C) 2017 Elsevier B.V. All rights reserved.
In this paper, we propose a branch-and-bound algorithm for finding a global optimal solution for a nonconvex quadratic program with convex quadratic constraints (NQPCQC). We first reformulate NQPCQC by adding some non...
详细信息
In this paper, we propose a branch-and-bound algorithm for finding a global optimal solution for a nonconvex quadratic program with convex quadratic constraints (NQPCQC). We first reformulate NQPCQC by adding some nonconvex quadratic constraints induced by eigenvectors of negative eigenvalues associated with the nonconvex quadratic objective function to Shor's semidefinite relaxation. Under the assumption of having a bounded feasible domain, these nonconvex quadratic constraints can be further relaxed into linear ones to form a special semidefinite programming relaxation. Then an efficient branch-and-bound algorithm branching along the eigendirections of negative eigenvalues is designed. The theoretic convergence property and the worst-case complexity of the proposed algorithm are proved. Numerical experiments are conducted on several types of quadratic programs to show the efficiency of the proposed method.
Real fretting fatigue cycles often involve complex loading where the fretting force may vary with a different phase or frequency to the other loads on the components. Analysis of the contact tractions in such cases ca...
详细信息
Real fretting fatigue cycles often involve complex loading where the fretting force may vary with a different phase or frequency to the other loads on the components. Analysis of the contact tractions in such cases can be difficult. Here we present a quadratic programming technique which enables the shear tractions to he determined in a relatively straightforward manner. A number of sample load histories are investigated and it is shown that the shear traction cycle rapidly shakes down to a steady state. Further the results are relatively insensitive to the manner in which loading is commenced.
This study proposes an integer quadratic programming method for grouping and selecting the singular spectral analysis components based on the empirical mode decomposition for performing the denoising. Here, the total ...
详细信息
This study proposes an integer quadratic programming method for grouping and selecting the singular spectral analysis components based on the empirical mode decomposition for performing the denoising. Here, the total number of the grouped singular spectral analysis components is equal to the total number of the intrinsic mode functions. The singular spectral analysis components are assigned to the group indexed by the corresponding intrinsic mode function where the two norm error between the corresponding intrinsic mode function and the sum of the grouped singular spectral analysis components is minimum. Actually, this assignment of the singular spectral analysis components to a particular group is an integer quadratic programming problem. However, the required computational power for finding the solution of the integer quadratic programming problem is high. On the other hand, by representing the integer quadratic programming problem as an integer linear programming problem and employing an existing numerical optimisation computer aided design tool for finding the solution of the integer linear programming problem, the solution can be found efficiently. Computer numerical simulation results are presented.
In this paper we introduce an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. The new feature of the proposed algorithm is the adaptive precision contr...
详细信息
In this paper we introduce an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. The new feature of the proposed algorithm is the adaptive precision control of the solution of auxiliary problems in the inner loop of the basic algorithm. Global convergence and boundedness of the penalty parameter are proved and an error estimate is given that does not have any term that accounts for the inexact solution of the auxiliary problems. Numerical experiments illustrate efficiency of the algorithm presented.
In this paper, we present an iterative quadratic programming approach to design stable IIR digital differentiator. At each iteration, the cost function is transformed into a quadratic form by treating the denominator ...
详细信息
In this paper, we present an iterative quadratic programming approach to design stable IIR digital differentiator. At each iteration, the cost function is transformed into a quadratic form by treating the denominator polynomial obtained from the preceding iteration as a part of the weighting function, and the pole radii are constrained to lie in the unit circle by using the implications of Rouche's theorem. After solving the standard quadratic programming problem at each iteration, the design algorithm converges to a stable and truly weighted least-squares solution. Design examples demonstrate that our method provides a better design results than the conventional quadratic programming method. (C) 2000 Elsevier Science B.V. All rights reserved.
Inertial appendages (e.g., tails and reaction wheels) have shown their reorientation capability to enhance robots' mobility while airborne or improve robots' safety in falling. The tail, especially with two De...
详细信息
Inertial appendages (e.g., tails and reaction wheels) have shown their reorientation capability to enhance robots' mobility while airborne or improve robots' safety in falling. The tail, especially with two Degrees of Freedom (DoFs), is normally subject to its limited Range of Motion (RoM). Although the reaction wheel circumvents this limitation, its efficiency has been shown lower than the tail in terms of inducing Moment of Inertia (MoI). In literature, only one type of inertial appendages has been used on terrestrial robots in the air, e.g., either using a tail on the hexapedal robot RHex or using a reaction wheel on the jumping quadruped robot SpaceBok. In this letter, to benefit from both unlimited RoM and efficient MoI-inducing, we propose combining a 1-DoF tail and a reaction wheel together for spatial reorientation (regulating the robot body's 3D orientation). Inspired by this, a hybrid tail-wheel robot is built, i.e., the tail that creates roll motion is attached to a wheel-equipped robot whose wheels act like a reaction wheel and generate pitch rotation;however, the robot is underactuated on the yaw rotation. To achieve its real-time spatial reorientation, we propose a novel quadratic programming algorithm based on a geometric metric for the underactuated hybrid tail-wheel robot. Within the proposed algorithm, the physical limitations on tail and wheel velocities are automatically accommodated. Numerical comparisons among wheel-wheel, tail-wheel, and 2-DoF tail robots showed the strength of the hybrid tail-wheel appendage on reorientation convergence and free of collision. Experimental results further demonstrated the capability of real-time spatial reorientation with underactuation and velocity constraints by using the combined tail-wheel inertial appendage.
暂无评论