Abstract
Stochastic quadratic programming with recourse is one of the most important topics in the field of optimization. It is usually assumed that the probability distribution of random variables has complete information, but only part of the information can be obtained in practical situation. In this paper, we propose a stochastic quadratic programming with imperfect probability distribution based on the linear partial information (LPI) theory. A direct optimizing algorithm based on Nelder-Mead simplex method is proposed for solving the problem. Finally, a numerical example is given to demonstrate the efficiency of the algorithm.
Highlights
Stochastic programming is an important method to solve decision problems in random environment
It is usually assumed that the probability distribution of random variables has complete information, but only part of the information can be obtained in practical situation
We propose a stochastic quadratic programming with imperfect probability distribution based on the linear partial information (LPI) theory
Summary
Stochastic programming is an important method to solve decision problems in random environment. With regard to the theory and methods of two-stage stochastic programming, a very systematic study has been conducted and many important solutions have been proposed [2] In these methods, the dual decomposition L-shape algorithm established in the literature [3] is the most effective algorithm for solving two-stage stochastic programming. The dual decomposition L-shape algorithm established in the literature [3] is the most effective algorithm for solving two-stage stochastic programming It is based on the duality theory, and the algorithm converges to the optimal solution by determining the feasible cutting plane and optimal cutting, and solving the main problem step by step. In [11], based on the linear partial information (LPI) theory of Kofler [12], a class of two-stage stochastic programming with recourse is established, and an L-shape method based on quadratic programming is given.
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