scholarly journals GS-OPT: A new fast stochastic algorithm for solving the non-convex optimization problem

2020 ◽  
Vol 9 (2) ◽  
pp. 183
Author(s):  
Xuan Bui ◽  
Nhung Duong ◽  
Trung Hoang
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Latent Dirichlet Allocation ◽  
Stochastic Algorithm ◽  
Inference Problem ◽  
Theoretical Understanding ◽  
Convex Optimization Problem ◽  
Discrete Probability ◽  
Convex Problems ◽  
Posterior Inference

<p>Non-convex optimization has an important role in machine learning. However, the theoretical understanding of non-convex optimization remained rather limited. Studying efficient algorithms for non-convex optimization has attracted a great deal of attention from many researchers around the world but these problems are usually NP-hard to solve. In this paper, we have proposed a new algorithm namely GS-OPT (General Stochastic OPTimization) which is effective for solving the non-convex problems. Our idea is to combine two stochastic bounds of the objective function where they are made by a commonly discrete probability distribution namely Bernoulli. We consider GS-OPT carefully on both the theoretical and experimental aspects. We also apply GS-OPT for solving the posterior inference problem in the latent Dirichlet allocation. Empirical results show that our approach is often more efficient than previous ones.</p>

scholarly journals Heliostat Field Layout Optimization with Evolutionary Algorithms

10.29007/7p6t ◽  
2018 ◽  
Author(s):  
Pascal Richter ◽  
David Laukamp ◽  
Levin Gerdes ◽  
Martin Frank ◽  
Erika Ábrahám
Keyword(s):  
Power Plant ◽  
Convex Optimization ◽  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Computer Science ◽  
Energy Supply ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
New Genotype

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant.We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals.Experimental results show the applicability of our approach.

scholarly journals Reconstruction of the early Universe as a convex optimization problem

2003 ◽  
Vol 346 (2) ◽  
pp. 501-524 ◽  
Author(s):  
Y. Brenier ◽  
U. Frisch ◽  
M. Hénon ◽  
G. Loeper ◽  
S. Matarrese ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Early Universe ◽  
Optimization Problem ◽  
Convex Optimization Problem

Design of Low Order Controllers for Decoupled MIMO Systems With Time Response Specifications

2018 ◽  
pp. 90-128
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Mimo Systems ◽  
Design Method ◽  
Optimal Solution ◽  
Time Response ◽  
Convex Optimization Problem ◽  
Tito Systems ◽  
Low Order

The design of a low order controller for decoupled MIMO systems is proposed. The main objective of this controller is to guarantee some closed loop time response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a non-convex optimization problem. In order to obtain an optimal solution, the use of a global optimization method is suggested. In this chapter, the proposed solution is the GGP method. The principle of this method consists of transforming a non-convex optimization problem to a convex one by some mathematical transformations. So as to accomplish the fixed goal, it is imperative to decouple the coupled MIMO systems. To approve the controllers' design method, the synthesis of fixed low order controller for decoupled TITO systems is presented firstly. Then, this design method is generalized in the case of MIMO systems. Simulation results and a comparison study between the presented approach and a PI controller are given in order to show the efficiency of the proposed controller. It is remarkable that the obtained solution meets the desired closed loop time specifications for each system output. It is also noted that by considering the proposed approach the user can fix the desired closed loop performances for each output independently.

scholarly journals Multitarget Linear-Quadratic Control Problem: Semi-Infinite Interval

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
L. Faybusovich ◽  
T. Mouktonglang
Keyword(s):  
Convex Optimization ◽  
Control Problem ◽  
Optimization Problem ◽  
Infinite Interval ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Convex Optimization Problem ◽  
Simple Convex ◽  
Linear Quadratic Control Problem

We consider multitarget linear-quadratic control problem on semi-infinite interval. We show that the problem can be reduced to a simple convex optimization problem on the simplex.

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