حول بعض طرائق الأمثلية العددية
On Some Numerical Optimization Methods
- الباحث
- نوفل شاكر كاظم عاشور
- المشرف
- احمد صباح الجيلاوي
- الجامعة
- جامعة بابل
- الكلية / القسم
- كلية التربية للعلوم الصرفة / الرياضيات
- الشهادة
- دكتوراه
- السنة
- 2022
- لغة الرسالة
- انكليزي
- الكلمات المفتاحية
- Numerical optimization; Optimization methods; Penalty function; Quadratic programming
Abstract
The goal of this dissertation is to find a better technique that converges faster. The strategy that used the type of approximate methods, we have discussed linear and non-linear optimization problems and how to convert problems from non-linear to linear problems using Lagrange equation. Also, study how to convert constrained optimization problems to unconstrained optimization problems by addition to the object function the penalty parameter, and then touched on other more common methods, which is the method of the augmented Lagrange, and compared the results of the two methods, we got good results to reach the optimal solution by using numerical analysis. However, found a better line search technique and different combinations of optimization and line search algorithm. Each iteration of a line search methods computes a search direction dk and then decides how far to move along that direction. The iteration is given by xk+1 = xk + αkdk where αk ≥0 and αk ∈R is called the step length. The prosperity of a line search methods depends on efficient choices of both the direction dk and right the step length αk. However, NP- problem especially( Portfolio Optimization Problem), using (GUROBI) via the provided Python interface and using regularization we found the solution is same to the original solution and if we using penalty method we will get approximates solutions using closed to optimal solution. However, choose a different problem from the Big Mac library and using two kinds of line searches are (HagerZhang Line search and BackTracking), to the same method Augmented Lagrangian a note the convergence to minimize take different behaviour also the same process in Penalty methods. If the change line search for the method will be got different results. After that, changed the line search methods and studied the approach behaviour to the optimal solution. Demonstrated that for each problem a line search methods must be chosen and that not all line search methods give the same results to solve the constrained problems, so it was clarified that line search methods have a significant impact on obtaining the desired results, in addition to all of the above. Proposed a mathematical formula to reduce the spread of the disease(Coronavirus) by best on a multiple objective functions, and also proposed a mathematical formula for transporting the vaccine from the United States source to the world. All results in this study were carried out using Python language.
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