On the stochastic optimization problems of plastic metal working processes under stochastic initial conditions

1999 ◽  
Vol 6 (1) ◽  
pp. 111-125
Author(s):  
Michael B. Gitman ◽  
Peter V. Trusov ◽  
Sergei A. Fedoseev
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Metal Working ◽  
Plastic Metal ◽  
Working Processes

On the stochastic optimization problems of plastic metal-working processes

1997 ◽  
Vol 84 (3) ◽  
pp. 1109-1112 ◽  
Author(s):  
M. B. Gitman ◽  
P. V. Trusov ◽  
S. A. Fedoseev
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Metal Working ◽  
Plastic Metal ◽  
Working Processes

scholarly journals On quantitative stability in infinite-dimensional optimization under uncertainty

2021 ◽  
Author(s):  
M. Hoffhues ◽  
W. Römisch ◽  
T. M. Surowiec
Keyword(s):  
Stochastic Optimization ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Under Uncertainty ◽  
Optimal Solutions ◽  
Probability Metrics ◽  
Pde Constrained Optimization ◽  
Quantitative Stability ◽  
Infinite Dimensional ◽  
Optimal Value

AbstractThe vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of the optimal value and optimal solutions on these approximations as the sample size increases or more data becomes available. Due to the weak convergence properties of sequences of probability measures, there is no guarantee that these quantities will exhibit favorable asymptotic properties. We consider a class of infinite-dimensional stochastic optimization problems inspired by recent work on PDE-constrained optimization as well as functional data analysis. For this class of problems, we provide both qualitative and quantitative stability results on the optimal value and optimal solutions. In both cases, we make use of the method of probability metrics. The optimal values are shown to be Lipschitz continuous with respect to a minimal information metric and consequently, under further regularity assumptions, with respect to certain Fortet-Mourier and Wasserstein metrics. We prove that even in the most favorable setting, the solutions are at best Hölder continuous with respect to changes in the underlying measure. The theoretical results are tested in the context of Monte Carlo approximation for a numerical example involving PDE-constrained optimization under uncertainty.

Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

2012 ◽  
Vol 215-216 ◽  
pp. 133-137
Author(s):  
Guo Shao Su ◽  
Yan Zhang ◽  
Zhen Xing Wu ◽  
Liu Bin Yan
Keyword(s):  
Stochastic Optimization ◽  
Covariance Matrix ◽  
Optimization Problems ◽  
Fitness Function ◽  
Optimization Methods ◽  
Evolution Strategy ◽  
Covariance Matrix Adaptation ◽  
Study Results ◽  
Highly Nonlinear ◽  
Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

Improvement of nonmonotone deformation technology in plastic metal working

2021 ◽  
pp. 115-122
Author(s):  
S.M. Vaytsekhovich ◽  
Yu.V. Vlasov ◽  
A.Yu. Zhuravlev
Keyword(s):  
Experimental Investigation ◽  
Simple Shear ◽  
Strain State ◽  
Effectiveness Evaluation ◽  
Inhomogeneous Body ◽  
Metal Working ◽  
Practical Application ◽  
Angular Pressing ◽  
Plastic Metal ◽  
Rational Sequence

The production of semi-finished products made of refractory metals is considered. The advantage of parts production using combination of two types of straining with change in the straining direction: direct extrusion and equal-channel pressing is shown. The experimental investigation data of pure and simple shear for the semi-finished products processing made of tungsten and molybdenum are presented. Requirements for the tool providing diagonal flow and angular straining are formulated based on the analysis of the stress-strain state of the processes of axial symmetric extrusion and simple shear of plastically inhomogeneous body. Effectiveness evaluation of the combination of various types of fixtures and the rational sequence for using of diagonal flow and angular pressing is given. Experimental devices for practical application of the proposed technology are developed.

Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

2021 ◽  
Author(s):  
Xiting Gong ◽  
Tong Wang
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
High Dimensional ◽  
Value Functions

Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochastic Optimization Problems

Primal–Dual Mirror Descent Method for Constraint Stochastic Optimization Problems

2018 ◽  
Vol 58 (11) ◽  
pp. 1728-1736 ◽  
Author(s):  
A. S. Bayandina ◽  
A. V. Gasnikov ◽  
E. V. Gasnikova ◽  
S. V. Matsievskii
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Descent Method ◽  
Mirror Descent Method ◽  
Mirror Descent ◽  
Primal Dual

scholarly journals Characterization of the Transient Response of Coupled Optimization in Multidisciplinary Design

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Erich Devendorf ◽  
Kemper Lewis
Keyword(s):  
Optimization Problems ◽  
Initial Conditions ◽  
Systems Design ◽  
Discrete Systems ◽  
Product Development Process ◽  
Multidisciplinary Design ◽  
Distributed Design ◽  
Equilibrium Solutions ◽  
Acceptable Solution ◽  
Number Of Iterations

Time is an asset of critical importance in a multidisciplinary design process and it is desirable to reduce the amount of time spent designing products and systems. Design is an iterative activity and designers consume a significant portion of the product development process negotiating a mutually acceptable solution. The amount of time necessary to complete a design depends on the number and duration of design iterations. This paper focuses on accurately characterizing the number of iterations required for designers to converge to an equilibrium solution in distributed design processes. In distributed design, systems are decomposed into smaller, coupled design problems where individual designers have control over local design decisions and seek to achieve their own individual objectives. These smaller coupled design optimization problems can be modeled using coupled games and the number of iterations required to reach equilibrium solutions varies based on initial conditions and process architecture. In this paper, we leverage concepts from game theory, classical controls, and discrete systems theory to evaluate and approximate process architectures without carrying out any solution iterations. As a result, we develop an analogy between discrete decisions and a continuous time representation that we analyze using control theoretic techniques.

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