On convergence rates of subgradient optimization methods

1977 ◽  
Vol 13 (1) ◽  
pp. 329-347 ◽  
Author(s):  
J. L. Goffin
Keyword(s):  
Convergence Rates ◽  
Optimization Methods ◽  
Subgradient Optimization

Sheet Thickness Optimization for Superplastic Forming of Engineering Structures

1999 ◽  
Vol 122 (1) ◽  
pp. 117-123 ◽  
Author(s):  
A. Huang ◽  
M. J. Cardew-Hall ◽  
A. Lowe
Keyword(s):  
Convergence Rates ◽  
Control Method ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Superplastic Forming ◽  
Optimization Methods ◽  
Gradient Search ◽  
Engineering Structures ◽  
Proportional Control ◽  
Control Approach

This paper explores two optimization strategies; the gradient search and proportional control methods, for determining the initial sheet thickness of superplastic forming to ensure final desired part thickness. A hemispherical dome model was involved in the testing of both optimization methods. Also, a three-dimensional rectangular box model was optimized by the proportional control method. The gradient search technique is shown to be acceptable in terms of the optimized thickness obtained, but displays poor convergence rates. The proportional control approach presented is easy to be implemented, and yields not only more accurate sheet thickness, but much higher convergence speeds that makes such optimization possible on complex geometric models. [S1087-1357(00)01001-7]

scholarly journals Convergence of Subtangent-Based Relaxations of Nonlinear Programs

Processes ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 221 ◽  
Author(s):  
Huiyi Cao ◽  
Yingkai Song ◽  
Kamil A. Khan
Keyword(s):  
Pointwise Convergence ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Convex Relaxation ◽  
Sufficient Conditions ◽  
Original System ◽  
Optimization Methods ◽  
Second Order ◽  
Nonlinear Programs ◽  
Outer Approximations

Convex relaxations of functions are used to provide bounding information to deterministic global optimization methods for nonconvex systems. To be useful, these relaxations must converge rapidly to the original system as the considered domain shrinks. This article examines the convergence rates of convex outer approximations for functions and nonlinear programs (NLPs), constructed using affine subtangents of an existing convex relaxation scheme. It is shown that these outer approximations inherit rapid second-order pointwise convergence from the original scheme under certain assumptions. To support this analysis, the notion of second-order pointwise convergence is extended to constrained optimization problems, and general sufficient conditions for guaranteeing this convergence are developed. The implications are discussed. An implementation of subtangent-based relaxations of NLPs in Julia is discussed and is applied to example problems for illustration.

scholarly journals A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

2016 ◽  
Vol 23 (2) ◽  
pp. 252-262 ◽  
Author(s):  
Nima NOII ◽  
Iman AGHAYAN ◽  
Iman HAJIRASOULIHA ◽  
Mehmet Metin KUNT
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Convergence Rates ◽  
Design Method ◽  
Optimization Methods ◽  
Cholesky Factorization ◽  
Truss Structures ◽  
Design Solution ◽  
Design Parameters ◽  
Traditional Design

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algo­rithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical exam­ples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications.

A Hybrid Hyper-heuristic Flower Pollination Algorithm for Service Composition Problem in IoT

2019 ◽  
Vol 13 ◽  
Author(s):  
Neeti Kashyap ◽  
A. Charan Kumari ◽  
Rita Chhikara
Keyword(s):  
Evolutionary Algorithm ◽  
Service Composition ◽  
Convergence Rates ◽  
Modern Science ◽  
Optimization Methods ◽  
Search Space ◽  
Flower Pollination Algorithm ◽  
The Novel ◽  
Flower Pollination ◽  
Composition Problem

Objectives: The modern science applications have non-continuous and multivariate nature due to which the traditional optimization methods suffer a lack of efficiency. Flower pollination is a natural interesting procedure in the real world. The novel optimization algorithms can be designed by employing the evolutionary capability of the flower pollination to optimize resources. Method: This paper introduces the hybrid algorithm named Hybrid Hyper-heuristic Flower Pollination Algorithm, HHFPA. It uses a combination of flower pollination algorithm (FPA) and Hyper-heuristic evolutionary algorithm (HypEA). This paper compares the basic FPA with the proposed algorithm named HHFPA. FPA is inspired by the pollination process of flowers whereas the hyper-heuristic evolutionary algorithm operates on the heuristics search space that contains all the heuristics to find a solution for a given problem. The proposed algorithm is implemented to solve the Quality of Service (QoS) based service composition Problem (SCoP) in Internet of Things (IoT). With increasing services with same functionality on the web, selecting a suitable candidate service based on non-functional characteristics such as QoS has become an inspiration for optimization. Results: This paper includes experimental results showing better outcomes to find the best solution using the proposed algorithm as compared to Basic FPA. Conclusion: The empirical analysis also reveals that HHFPA outperformed basic FPA in solving the SCoP with more convergence rates.

Sign in / Sign up

Export Citation Format

Share Document