scholarly journals Solving Two Stage Stochastic Programming Problems Using ADMM

2021 ◽  
Author(s):  
Nouralden Mohammed ◽  
Montaz Ali
Keyword(s):  
Stochastic Programming ◽  
Programming Problem ◽  
Lower Semicontinuity ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Performance Criteria ◽  
Benchmark Problems ◽  
Two Stage ◽  
Progressive Hedging ◽  
Separable Optimization

Abstract In this paper, we have dealt with the solution of a two-stage stochastic programming problem using ADMM. We have formulated the problem into a deterministic three-block separable optimization problem, and then we applied ADMM to solve it. We have established the theoretical convergence of ADMM to the optimal solution based on the concept of lower semicontinuity and the Kurdyka-Lojasiewicz property. We have compared ADMM with Progressive Hedging in terms of performance criteria using five benchmark problems from the literature. The comparison shows that ADMM outperforms Progressive Hedging.

Polynomial Approximation for Two Stage Stochastic Programming with Separable Objective

2012 ◽  
pp. 322-333
Author(s):  
Lijian Chen ◽  
Dustin J. Banet
Keyword(s):  
Monte Carlo ◽  
Stochastic Programming ◽  
Monte Carlo Simulations ◽  
Programming Model ◽  
Optimal Solution ◽  
Two Stage ◽  
Convex Objective Function ◽  
Stochastic Programming Model ◽  
Gradient Type ◽  
Norm Approximation

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polynomial is constructed by Bernstein polynomial and norm approximation models. At a given accuracy, the necessary degree of the polynomial and the replications are properly determined. Afterward, the authors applied the first gradient type algorithms on the new stochastic programming model with the polynomial objective, resulting in the optimal solution being attained.

scholarly journals Beberapa Metode pada Masalah Pemrograman Stokastik

2017 ◽  
Vol 3 (2) ◽  
pp. 83-86
Author(s):  
Ihda Hasbiyati ◽  
Hasriati Hasriati
Keyword(s):  
Stochastic Programming ◽  
Programming Problem ◽  
Mathematical Problem ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Stochastic Programming Problem ◽  
Shape Decomposition ◽  
Reasonable Solution ◽  
Stochastic Data ◽  
Stochastic Element

Stochastic programming problem is mathematical problem (linear, integer, mixed integer, and nonlinier) with stochastic element lies data. To get reasonable solution and optimal with its stochastic data is needed several method.  Applicable method in trouble stochastic programming are L-Shape decomposition and lagrange decomposition. Each method can determine optimal solution to troubleshoots stochastic programming

Polynomial Approximation for Two Stage Stochastic Programming with Separable Objective

2010 ◽  
Vol 1 (3) ◽  
pp. 75-88 ◽  
Author(s):  
Lijian Chen ◽  
Dustin J. Banet
Keyword(s):  
Monte Carlo ◽  
Stochastic Programming ◽  
Bernstein Polynomial ◽  
Programming Model ◽  
Optimal Solution ◽  
Two Stage ◽  
Convex Objective Function ◽  
Stochastic Programming Model ◽  
Gradient Type ◽  
Norm Approximation

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polynomial is constructed by Bernstein polynomial and norm approximation models. At a given accuracy, the necessary degree of the polynomial and the replications are properly determined. Afterward, the authors applied the first gradient type algorithms on the new stochastic programming model with the polynomial objective, resulting in the optimal solution being attained.

scholarly journals The Artificial Neural Networks Based on Scalarization Method for a Class of Bilevel Biobjective Programming Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Tao Zhang ◽  
Zhong Chen ◽  
June Liu ◽  
Xiong Li
Keyword(s):  
Programming Problem ◽  
Practical Problem ◽  
Optimization Problem ◽  
Classical Literature ◽  
Two Stage ◽  
Scalarization Method ◽  
Biobjective Optimization ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
Biobjective Programming

A two-stage artificial neural network (ANN) based on scalarization method is proposed for bilevel biobjective programming problem (BLBOP). The induced set of the BLBOP is firstly expressed as the set of minimal solutions of a biobjective optimization problem by using scalar approach, and then the whole efficient set of the BLBOP is derived by the proposed two-stage ANN for exploring the induced set. In order to illustrate the proposed method, seven numerical examples are tested and compared with results in the classical literature. Finally, a practical problem is solved by the proposed algorithm.

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