We consider general, typically nonconvex, quadratic programming Problems. The Semi-definite relaxation proposed by Shor provides bounds on the optical solution. but it does not always provide sufficiently strong bound...
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We consider general, typically nonconvex, quadratic programming Problems. The Semi-definite relaxation proposed by Shor provides bounds on the optical solution. but it does not always provide sufficiently strong bounds if linear constraints are also involved. To get rid of the linear side-constraints. another, stronger convex relaxation is derived. This relaxation uses copositive matrices. Special cases are discussed for which both relaxations are equal. At the end of the paper, the complexity and solvability of the relaxations are discussed.
Despite safe mechanical design is necessary for the collaborative robots, we can not underestimate the importance of active safety due to a multi-objective control design. Active safety not only complements the mechan...
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Despite safe mechanical design is necessary for the collaborative robots, we can not underestimate the importance of active safety due to a multi-objective control design. Active safety not only complements the mechanical compliance but also enables classical industrial robots the ability to fulfill additional task-space objectives. Using the gradient of the collision avoidance task as hard constraints of a quadratic programming (QP) controller, we assign strict priority to avoid collisions and specify other QP controller objectives with soft task priorities. Through experiments performed on a dual-arm robot, we show that the proposed solution is able to generate safe robot motion that fulfills the task specifications while keeping the feasibility of the underlying quadratic optimization problem.
We propose a branch and bound reduced algorithm for quadratic programming problems with quadratic constraints. In this algorithm, we determine the lower bound of the optimal value of original problem by constructing a...
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We propose a branch and bound reduced algorithm for quadratic programming problems with quadratic constraints. In this algorithm, we determine the lower bound of the optimal value of original problem by constructing a linear relaxation programming problem. At the same time, in order to improve the degree of approximation and the convergence rate of acceleration, a rectangular reduction strategy is used in the algorithm. Numerical experiments show that the proposed algorithm is feasible and effective and can solve small-and medium-sized problems.
In this study, a fuzzy two-stage quadratic programming (FTSQP) method is developed for planning waste-management systems under uncertainty. It incorporates approaches of fuzzy quadratic programming and two-stage stoch...
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In this study, a fuzzy two-stage quadratic programming (FTSQP) method is developed for planning waste-management systems under uncertainty. It incorporates approaches of fuzzy quadratic programming and two-stage stochastic programming within a general optimization framework, to better reflect uncertainties expressed as probability-density and fuzzy-membership functions. The FTSQP can be used for analyzing various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. Moreover, using fuzzy quadratic terms rather than linear ones, the proposed method can improve upon the existing fuzzy linear programs through (a) more effectively optimizing the general satisfaction of the objective and constraints, (b) minimizing the variation of satisfaction degrees among the constraints and leading to more robust solutions, and (c) reflecting the trade-off between the system cost and the constraint-violation risk. The developed method is applied to a case Study of municipal solid waste management. The results indicate that reasonable solutions have been generated. They will allow in-depth analyses of trade-offs between environmental and economic objectives as well as those between system cost and decision-maker's satisfaction degree.
A new discrete-time neural network is proposed for solving convex quadratic programming problems with hybrid constraints. Based on the projection operator and convex optimization technologies, a single layer discrete-...
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A new discrete-time neural network is proposed for solving convex quadratic programming problems with hybrid constraints. Based on the projection operator and convex optimization technologies, a single layer discrete-time neural network with monotonic descent dynamic step sizes is constructed. It is proved that the equilibrium points of the discrete-time neural network are globally exponentially convergent to the optimal solutions of the programming problem. Moreover, an algorithm is given based on the proposed neural network and the scheme of backtracking step-size adaptation. Finally, the proposed algorithm is applied to three types of quadratic programming problems and the gas oven identification via a support vector regression algorithm. The numerical experiments are performed to show the correctness and effectiveness of the results in this paper.
quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes more computationally demanding, and new algorithms are needed t...
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quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes more computationally demanding, and new algorithms are needed to efficiently solve them at massive scales. Targeting large-scale problems, we develop a multiagent quadratic programming framework in which each agent updates only a small number of the total decision variables in a problem. Agents communicate their updated values to each other, though we do not impose any restrictions on the timing with which they do so, nor on the delays in these transmissions. Furthermore, we allow agents to independently choose their stepsizes, subject to mild restrictions. We further provide the means for agents to independently regularize the problems they solve, thereby improving convergence properties while preserving agents' independence in selecting parameters. Larger regularizations accelerate convergence but increase the error in the solution obtained, and we quantify the tradeoff between convergence rates and quality of solutions. Simulation results are presented to illustrate these developments.
The main focus of this paper is a method for real-time optimization of the gear shift trajectories for electric vehicles (EVs) with dual clutch transmissions. First, a driveline model was arranged for each gear shift ...
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The main focus of this paper is a method for real-time optimization of the gear shift trajectories for electric vehicles (EVs) with dual clutch transmissions. First, a driveline model was arranged for each gear shift process. The states in each gear shift process can be predicted through these models. An objective function is composed of a frequency-shaped jerk to minimize the shift shock and take into account the bandwidth limit of the lower-level controller. Equality constraints are defined for smooth model changes during the gear shift processes. Moreover, the conditions needed to reflect the driver's pedal input (which can be changed in real-time) is composed of an equality constraint. In addition, inequality constraints are constructed to limit the maximum value of the torque, torque rate, and jerk during gear shift processes. Finally, the problem is formulated in quadratic programming (QP) form. The gear shift trajectories and feedforward inputs are generated by obtaining an optimal solution through the QP solver. The performance of the proposed algorithm is verified through testbench experiments.
This article introduces a solution for the dynamic economic dispatch problem using a hybrid technique of the Hopfield neural network and quadratic programming. This hybrid algorithm is based on using the enhanced Hopf...
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This article introduces a solution for the dynamic economic dispatch problem using a hybrid technique of the Hopfield neural network and quadratic programming. This hybrid algorithm is based on using the enhanced Hopfield neural network to solve the static part of the problem and the quadratic programming algorithm for solving the dynamic part of the dynamic economic dispatch. This technique guarantees the global optimality of the solution due to its look-ahead capability. The proposed technique is applied to and tested on an example from the literature, and the solution is then compared with that obtained by some other techniques to prove the validity and effectiveness of the proposed algorithm.
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bo...
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Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal-dual form. The primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero. The dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities. In each of these methods, the search directions satisfy a KKT system of equations formed from Hessian and constraint components associated with an appropriate column basis. The composition of the basis is specified by an active-set strategy that guarantees the nonsingularity of each set of KKT equations. Each of the proposed methods is a conventional active-set method in the sense that an initial primal- or dual-feasible point is required. In the second part of the paper, it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple-bound constraints and adding a penalty term to the objective function. Any conventional column basis may be made optimal for such a primal-dual pair of shifted-penalized problems. The shifts are then updated using the solution of either the primal or the dual shifted problem. An obvious application of this approach is to solve a shifted dual QP to define an initial feasible point for the primal (or vice versa). The computational performance of each of the proposed methods is evaluated on a set of convex problems from the CUTEst test collection.
In this paper, a new projection neural network with two time delays is proposed for solving quadratic-programming problems subject to linear constraints. And we give the existence of the continuous solution. By the th...
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In this paper, a new projection neural network with two time delays is proposed for solving quadratic-programming problems subject to linear constraints. And we give the existence of the continuous solution. By the theory of functional differential equation, the proposed neural network is proved to be globally exponentially stable under some conditions. Simulation results with some applications show the performance and characteristic of the proposed neural network. (C) 2012 Elsevier Inc. All rights reserved.
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