Flattened aggregate function method for nonlinear programming with many complicated constraints

2020 ◽  
Vol 86 (1) ◽  
pp. 103-122
Author(s):  
Xiaowei Jiang ◽  
Yueting Yang ◽  
Yunlong Lu ◽  
Mingyuan Cao
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yaming Ren

With the continuous development of the world economy, the development and utilization of environmentally friendly and renewable energy have become the trend in many countries. In this paper, we study the dynamic economic dispatch with wind integrated. Firstly, we take advantage of the positive and negative spinning reserve to deal with wind power output prediction errors in order to establish a dynamic economic dispatch model of wind integrated. The existence of a min function makes the dynamic economic dispatch model nondifferentiable, which results in the inability to directly use the traditional mathematical methods based on gradient information to solve the model. Inspired by the aggregate function, we can easily transform the nondifferentiable model into a smooth model when parameter p tends to infinity. However, the aggregate function will cause data overflow when p tends to infinity. Then, for solving this problem, we take advantage of the adjustable entropy function method to replace of aggregate function method. In addition, we further discuss the adjustable entropy function method and point out that the solution generated by the adjustable entropy function method can effectively approximate the solution of the original problem without parameter p tending to infinity. Finally, simulation experiments are given, and the simulation results prove the effectiveness and correctness of the adjustable entropy function method.


1977 ◽  
Vol 99 (1) ◽  
pp. 31-36 ◽  
Author(s):  
S. B. Schuldt ◽  
G. A. Gabriele ◽  
R. R. Root ◽  
E. Sandgren ◽  
K. M. Ragsdell

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.


2020 ◽  
Vol 7 (1) ◽  
pp. 84-87
Author(s):  
Galina E. Egorova ◽  
Tatyana S. Zaitseva

The penalty function method is one of the most popular and universal methods of convex programming and belongs to the group of indirect methods for solving nonlinear programming problems. Thе article discusses the algorithm for solving problems by the penalty function method, provides an example of a solution. A complete definition of the concepts used in the theoretical material of the method, and examples of its application are also given. It is worth noting that these methods are widely used to solve technical and economic problems. Also they are quite often used both in theoretical research and in the development of algorithms. The result of the work is the development of software for solving problems using the penalty function method.


Author(s):  
Umesh R. Patil ◽  
Prakash Krishnaswami

Abstract In designing a kinematic system, it is desirable to ensure that the performance of the system is relatively insensitive to small changes in the nominal design, since this will result in a more robust system that can be manufactured economically with looser tolerances. A general method for minimizing the sensitivity of such systems is developed in this paper. The approach is based on the idea of converting the minimum sensitivity design problem into a nonlinear programming problem which is then solved using an exterior penalty function method. The constrained multi-element formulation is used for kinematic analysis and sensitivity analysis is performed using a direct differentation technique. The resulting algorithm is general enough to handle any planar kinematic system. The proposed method has been implemented in a computer program which has been tested on some sample problems. The results provide convincing proof of the power and feasibility of this method.


2014 ◽  
Vol 1023 ◽  
pp. 187-191
Author(s):  
Feng Yun He ◽  
Fan Wang

The process of multi-back after blending water from one station is used in a block of Daqing oilfield, for saving energy, reducing consumption and easy to manage. For this block’s water blending system, research on its blending parameters optimization is carried on. According to the block’s characteristic of the process, the characteristic of energy cost minimum as objective function, setting up the multi-back after blending water from one station system’s parameter optimization mathematical model[1]. The model belongs to nonlinear programming problems with constraints, the mixed penalty function method and the improved conjugate direction method are used to solve the model, the optimum water blending temperature is determined by optimization calculating as 62.1°C and quantity of blending water a year is 1.13×105 t . By doing so, running costs saved 220,000 yuan per year to achieve the goal of saving energy and reducing consumption.


2014 ◽  
Vol 989-994 ◽  
pp. 2398-2401
Author(s):  
Xiao Wei Jiang ◽  
Yue Ting Yang ◽  
Yun Long Lu

A method of multiplier is presented for solving optimization problems. For large-scale constraint problems, combining the active set strategy, we use the aggregate function to approximate the max-value function. Only a few of functions are involved at each iteration, so the computation for gradient is significantly reduced. The numerical results show that the method is effective.


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