scholarly journals Some Unconstrained Optimization Methods

2019 ◽  
Author(s):  
Snezana S. Djordjevic
Keyword(s):  
Unconstrained Optimization ◽  
Optimization Methods

A Comparative Evaluation of Unconstrained Optimization Methods Applied to the Thermal Tomography Problem

1985 ◽  
Vol 107 (3) ◽  
pp. 228-233 ◽  
Author(s):  
S. T. Clegg ◽  
R. B. Roemer
Keyword(s):  
Unconstrained Optimization ◽  
Blood Perfusion ◽  
Optimization Methods ◽  
Sensitivity Study ◽  
Initial Guess ◽  
Optimization Techniques ◽  
Temperature Fields ◽  
Tissue Temperature ◽  
Initial Attempt ◽  
Error Space

In cancer hyperthermia treatments, it is important to be able to predict complete tissue temperature fields from sampled temperatures taken at the limited number of locations allowed by clinical constraints. An initial attempt to do this automatically using unconstrained optimization techniques to minimize the differences between experimental temperatures and temperatures predicted from treatment simulations has been previously reported [1]. This paper reports on a comparative study which applies a range of different optimization techniques (relaxation, steepest descent, conjugate gradient, Gauss, Box-Kanemasu, and Modified Box-Kanemasu) to this problem. The results show that the Gauss method converges more rapidly than the others, and that it converges to the correct solution regardless of the initial guess for the unknown blood perfusion vector. A sensitivity study of the error space is also performed, and the relationships between the error space characteristics and the comparative speeds of the optimization techniques are discussed.

A new hybrid conjugate gradient method of unconstrained optimization methods

2021 ◽  
pp. 2250070
Author(s):  
Chenna Nasreddine ◽  
Sellami Badreddine ◽  
Belloufi Mohammed
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Convex Combination ◽  
Optimization Methods ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

In this paper, we present a new hybrid method to solve a nonlinear unconstrained optimization problem by using conjugate gradient, which is a convex combination of Liu–Storey (LS) conjugate gradient method and Hager–Zhang (HZ) conjugate gradient method. This method possesses the sufficient descent property with Strong Wolfe line search and the global convergence with the strong Wolfe line search. In the end of this paper, we illustrate our method by giving some numerical examples.

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