scholarly journals Calmness in Optimization Problems with Equality Constraints

1995 ◽  
Vol 189 (2) ◽  
pp. 502-513 ◽  
Author(s):  
S. Di ◽  
R. Poliquin
Keyword(s):  
Optimization Problems ◽  
Equality Constraints

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

scholarly journals On the equality constraints tolerance of Constrained Optimization Problems

2014 ◽  
Vol 551 ◽  
pp. 55-65 ◽  
Author(s):  
Chengyong Si ◽  
Jing An ◽  
Tian Lan ◽  
Thomas Ußmüller ◽  
Lei Wang ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Equality Constraints ◽  
Constrained Optimization Problems

An Alternative Formulation of Collaborative Optimization Based on Geometric Analysis

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Xiang Li ◽  
Changan Liu ◽  
Weiji Li ◽  
Teng Long
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Geometric Analysis ◽  
Equality Constraints ◽  
Collaborative Optimization ◽  
System Level ◽  
Alternative Formulation ◽  
Linear Approximations ◽  
Engineering Design Problems ◽  
Level Problem

Collaborative optimization (CO) is a multidisciplinary design optimization (MDO) method with bilevel computational structure, which decomposes the original optimization problem into one system-level problem and several subsystem problems. The strategy of decomposition in CO is a useful way for solving large engineering design problems. However, the computational difficulties caused by the system-level consistency equality constraints hinder the development of CO. In this paper, an alternative formulation of CO called CO with combination of linear approximations (CLA-CO) is presented based on the geometric analysis of CO, which is more intuitive and direct than the previous algebraic analysis. In CLA-CO, the consistency equality constraints in CO are replaced by linear approximations to the subsystem responses. As the iterative process goes on, more linear approximations are added into the system level. Consequently, the combination of these linear approximations makes the system-level problem gradually approximate the original problem. In CLA-CO, the advantages of the decomposition strategy are maintained while the computational difficulties of the conventional CO are avoided. However, there are still difficulties in applying the presented CLA-CO to problems with nonconvex constraints. The application of CLA-CO to three optimization problems, a numerical test problem, a composite beam design problem, and a gear reducer design problem, illustrates the capabilities and limitations of CLA-CO.

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