scholarly journals Optimal solution approximation for infinite positive-definite quadratic programming

1995 ◽  
Vol 85 (2) ◽  
pp. 235-248 ◽  
Author(s):  
P. Benson ◽  
R. L. Smith ◽  
I. E. Schochetman ◽  
J. C. Bean
Keyword(s):  
Quadratic Programming ◽  
Optimal Solution ◽  
Positive Definite

A polynomial algorithm for the quadratic programming problem

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Valentin A. Bereznev
Keyword(s):  
Computational Complexity ◽  
Quadratic Form ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Polynomial Complexity ◽  
Polynomial Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Quadratic Programming Problem ◽  
Convex Polyhedral Cone

AbstractAn approach based on projection of a vector onto a pointed convex polyhedral cone is proposed for solving the quadratic programming problem with a positive definite matrix of the quadratic form. It is proved that this method has polynomial complexity. A method is said to be of polynomial computational complexity if the solution to the problem can be obtained in N

A Parallel Dual Projection Algorithm for Solving Positive Definite Quadratic Programming Problems

1990 ◽  
Author(s):  
Yugang Wang ◽  
Eric Sandgren
Keyword(s):  
Quadratic Programming ◽  
Positive Definite ◽  
Parallel Computer ◽  
Projection Algorithm ◽  
Test Problems ◽  
Local Optimum ◽  
Active Constraint ◽  
Search Point ◽  
Quadratic Programming Problems ◽  
Dual Projection

Abstract Two parallel algorithms, a dual projection algorithm and a hybrid dual projection algorithm, are proposed for solving positive definite quadratic programming problems. In each iteration of the algorithms, the search point is always a local optimum point on the current active constraint basis for both adding and dropping constraint operations. The advantage of this strategy is that the computation is stable and all operations maintain parallel properties. Only a pseudo-inverse matrix must be updated instead of two matrices in Goldfarb’s dual algorithm in a basis change. Both computational and space complexities are reduced by about half. When the search point reaches a vertex in the dual space, a pivot operation is employed to update the basis in the hybrid dual projection algorithm in place of the addition and deletion operations in the dual projection algorithm. This reduces the computational complexity by half in future iterations. Some suggestions are presented to further enhance the computational speed of the algorithm. Numerical results are presented based on randomly generated test problems. Comparison with other methods demonstrates that the new algorithm is efficient and stable and points to the possibility of implementation on a parallel computer.

scholarly journals Semi-Active Control for Two-Body Ocean Wave Energy Converter by Using Hybrid Model Predictive Control

2018 ◽  
Author(s):  
Qiuchi Xiong ◽  
Xiaofan Li ◽  
Dillon Martin ◽  
Sijing Guo ◽  
Lei Zuo
Keyword(s):  
Quadratic Programming ◽  
Active Control ◽  
Predictive Control ◽  
Wave Energy ◽  
Control Strategy ◽  
Optimal Solution ◽  
Energy Converter ◽  
Negative Power ◽  
Ocean Wave Energy ◽  
Power Maximization

Model predictive control (MPC) has been considered as one important feed-forward optimal control strategy for ocean wave energy converter (WEC) targeted on power maximization. The capability of MPC to handle system constraints (ex. stroke, velocity, actuator limitations), and the availability to provide optimal solution for linear system provide potential for the implementation of such algorithm in the WEC control. However, currently, only active MPC control has been introduced for single and two-body WECs. Such control strategy may introduce negative power during the optimization process, since the power take-off (PTO) damping has no constraint. In this paper, we proposed a hybrid MPC strategy in limiting both the PTO damping force and PTO damping to avoid negative power generation during cost function minimization (negative power minimization) for the two-body WEC. The problem is formulated into a quadratic programming (QP) problem targeted at power maximization. However, the standard QP problem formulation cannot be directly applied to the semi-active control problem due to the PTO damping constraints. Therefore, the problem is reformulated as a Mixed-integer Quadratic Programming (MIQP) problem, which contains logical switch to select constraint matrices based on the sign of the relative velocity between the buoy and submerged body. The optimal solution is compared with those of the active MPC control strategy and the passive model with the same irregular wave input.

scholarly journals Voltage and Reactive Power Optimization Using a Simplified Linear Equations at Distribution Networks with DG

Energies ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3334
Author(s):  
Seok-Il Go ◽  
Sang-Yun Yun ◽  
Seon-Ju Ahn ◽  
Joon-Ho Choi
Keyword(s):  
Quadratic Programming ◽  
Reactive Power ◽  
Linear Equations ◽  
Optimal Solution ◽  
Voltage Control ◽  
Distribution Networks ◽  
Mixed Integer ◽  
Voltage Variation ◽  
The Matrix ◽  
Control Devices

In this paper, the VVO (Volt/Var optimization) is proposed using simplified linear equations. For fast computation, the characteristics of voltage control devices in a distribution system are expressed as a simplified linear equation. The voltage control devices are classified according to the characteristics of voltage control and represented as the simplified linear equation. The estimated voltage of distribution networks is represented by the sum of the simplified linear equations for the voltage control devices using the superposition principle. The voltage variation by the reactive power of distributed generations (DGs) can be expressed as the matrix of reactance. The voltage variation of tap changing devices can be linearized into the control area factor. The voltage variation by capacitor banks can also be expressed as the matrix of reactance. The voltage equations expressed as simplified linear equations are formulated by quadratic programming (QP). The variables of voltage control devices are defined, and the objective function is formulated as the QP form. The constraints are set using operating voltage range of distribution networks and the control ranges of each voltage control device. In order to derive the optimal solution, mixed-integer quadratic programming (MIQP), which is a type of mixed-integer nonlinear programming (MINLP), is used. The optimal results and proposed method results are compared by using MATLAB simulation and are confirmed to be close to the optimal solution.

scholarly journals On the closure of the sum of closed subspaces

2001 ◽  
Vol 26 (5) ◽  
pp. 257-267 ◽  
Author(s):  
Irwin E. Schochetman ◽  
Robert L. Smith ◽  
Sze-Kai Tsui
Keyword(s):  
Hilbert Space ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
The Other ◽  
Quadratic Programming Problem ◽  
Orthogonal Projections ◽  
The Cost ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of the relevant orthogonal projections. As a consequence, we obtain sufficient conditions for the existence of an optimal solution to an abstract quadratic programming problem in terms of the kernels of the cost and constraint operators.

scholarly journals Semiconductor Yield Forecasting Using Quadratic-Programming-Based Fuzzy Collaborative Intelligence Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Toly Chen ◽  
Yu-Cheng Wang
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Programming ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Expert Opinions ◽  
Forecasting Methods ◽  
Global Optimal ◽  
Yield Forecasting ◽  
Collaborative Intelligence ◽  
Intelligence Approach

Several recent studies have proposed fuzzy collaborative forecasting methods for semiconductor yield forecasting. These methods establish nonlinear programming (NLP) models to consider the opinions of experts and generate fuzzy yield forecasts. Such a practice cannot distinguish between the different expert opinions and can not easily find the global optimal solution. In order to solve some problems and to improve the performance of semiconductor yield forecasting, this study proposes a quadratic-programming- (QP-) based fuzzy collaborative intelligence approach.

scholarly journals Unconstrained Quadratic Programming Problem with Uncertain Parameters

2021 ◽  
pp. 1-7
Author(s):  
Sie Long Kek ◽  
Fong Peng Lim ◽  
Harley Ooi
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Linear Equations ◽  
Optimal Solution ◽  
Theoretical Work ◽  
Quadratic Programming Problem ◽  
Model Parameters ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Unconstrained Quadratic Programming

In this paper, an unconstrained quadratic programming problem with uncertain parameters is discussed. For this purpose, the basic idea of optimizing the unconstrained quadratic programming problem is introduced. The solution method of solving linear equations could be applied to obtain the optimal solution for this kind of problem. Later, the theoretical work on the optimization of the unconstrained quadratic programming problem is presented. By this, the model parameters, which are unknown values, are considered. In this uncertain situation, it is assumed that these parameters are normally distributed; then, the simulation on these uncertain parameters are performed, so the quadratic programming problem without constraints could be solved iteratively by using the gradient-based optimization approach. For illustration, an example of this problem is studied. The computation procedure is expressed, and the result obtained shows the optimal solution in the uncertain environment. In conclusion, the unconstrained quadratic programming problem, which has uncertain parameters, could be solved successfully.

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