Optimallaşdırma üsullarıSyllabus

Subject code

İF-40171y

Credits

5

Student workload

150

Semester

Autumn semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat - mühazirə b) 30 saat - seminar

Out-of-class hours

a) 54 saat - sərbəst iş b) 36 saat - hazırlıq

“optimallaşdırma üsulları” fənni optimallaşdırma nəzəriyyəsinin əsas anlayışlarını, bir və çoxdəyişənli funksiyaların ekstremumunun tapılması üsullarını, şərti ekstremum məsələlərini və laqranj vurucuları metodunu əhatə edir. fənn çərçivəsində qabarıq çoxluqlar və qabarıq proqramlaşdırma, kun-takker teoremi, qradiyent və cərimə funksiyaları üsulları, klassik variasiya məsələləri, eyler tənliyi, funksionalın variasiyası, lejandr şərti, optimal idarəetmə nəzəriyyəsi və pontryaqinin maksimum prinsipi öyrənilir. kurs tələbələrdə optimallaşdırma məsələlərinin riyazi modelləşdirilməsi, müasir optimallaşdırma alqoritmlərinin tətbiqi və müxtəlif mühəndislik, informasiya texnologiyaları və idarəetmə sahələrində rast gəlinən praktiki problemlərin həlli üzrə nəzəri bilik və praktik bacarıqlar formalaşdırır.

• lecture
• interactive discussion
• seminar
• presentations

1. 1

   CLO 1: Must acquire knowledge about the necessary conditions and sufficient conditions for the extremum of univariate and multivariable functions.

2. 2

   CLO 2: Must know conditional extremum and lagrangian method of indefinite multiplication.

3. 3

   CLO 3: Must know convex sets, convex functions and their properties, linear and convex programming problems and their solutions, kuhn-tucker theorem.

4. 4

   CLO 4: Must learn gradient method and penalty function method.

5. 5

   CLO 5: Must know classical variational problems, euler's equation, second variation of functional and legendre's condition.

6. 6

   CLO 6: Must have knowledge of elements of optimal control theory, pontryagin's maximum principle and its discrete analogue.

1. 1.
   Formulation of optimization problems.Lecture

   In the subject, the concept of flow in the network, source, outlet, capacity and flow restrictions are studied. the mathematical formulation of the maximal flow problem and its role as an optimization problem in graph theory are explained. also, basic algorithmic approaches for finding extreme flow and the flow-cross-section relationship are explored.

2. 2.
   Unconditional extremum problem for univariate functions.Lecture

   In the subject, the issue of finding the maximum and minimum values ​​of a univariate function without any additional conditions is studied. the critical points of the function, the cases where the derivative is equal to zero or does not exist, are explained. also, determination of local extrema of the function is investigated based on the necessary and sufficient conditions of the extremum.

3. 3.
   One-dimensional classical conditional extremum problemLecture

   The issue of finding the maximum and minimum values ​​of a univariate function within a given additional condition is studied in the topic. mathematical setting of conditional extremum, possible solution area and rules for determining extremum points are explained. also, based on the classical approach, consideration of the condition and analysis of the obtained results are investigated.

4. 4.
   One-dimensional optimization methods.Lecture

   Finding the minimum and maximum values ​​of a univariate function by numerical methods is studied in the subject. the application principles of piece narrowing, golden ratio, dichotomy and other one-dimensional search methods are explained. the methods are also investigated for their accuracy, aggregation, and use in relevant optimization problems.

5. 5.
   A gradient method for a one-dimensional optimization problem.Lecture

   The subject studies the essence of the gradient method for finding the extremum of a univariate function. the choice of search direction and step length using the derivative of a function is explained. also, the application of the gradient method to clustering, accuracy and optimization problems is investigated.

6. 6.
   A geometric interpretation of a linear programming problem.Lecture

   In the subject, the geometrical description of the linear programming problem is studied based on the objective function and the system of constraints. representation of constraints in the form of half-planes on the plane and construction of the region of possible solutions is explained. also, the principle of searching for the optimal solution at the vertices of the feasible domain is investigated.

7. 7.
   Simplex methodLecture

   Solving linear programming problems by the simplex method is studied in the subject. rules for constructing a simplex table, selecting a leading column and a leading row are explained. finding the optimal solution and interpreting the results of the simplex method in an economic-mathematical sense are also investigated.

8. 8.
   Prominent clustersLecture

   The concept of convex set and its geometric meaning are studied in the topic. the condition that the set is convex is explained when the piece connecting two points is included in that set. the application of convex sets in optimization problems and linear programming is also investigated.

9. 9.
   Convex functions.Lecture

   The concept of convex function and its geometric meaning are studied in the topic. determining the convexity of a function by means of derivatives and convex sets is explained. also, the role of convex functions in finding their minimum points in optimization problems is investigated.

10. 10.
    A convex programming problem.Lecture

    In the subject, the mathematical formulation of optimization problems with prominent objective function and constraints is studied. in the case of convex programming, the property of the local minimum being the global minimum is explained. also, the basic conditions and application fields used in solving convex optimization problems are investigated.

11. 11.
    The stock market issue.Lecture

    In the topic, the mathematical formulation and main features of the bolsa problem are studied in the theory of optimization. it is explained that the objective functional consists of integral and boundary limits, as well as finding the extremum within the given limits.

12. 12.
    Unconditional extremum problem for a bivariate function.Lecture

    Finding the maximum and minimum values ​​of a bivariate function without additional restrictions is studied in the subject. the determination of stationary points and the investigation of extremum by means of special derivatives of the second order are explained. the rules for distinguishing local maximum, local minimum and saddle points are also investigated.

13. 13.
    Conditional extremum problem for a bivariate functionLecture

    The subject studies how to find the maximum and minimum values ​​of a bivariate function within the given restriction condition. the mathematical formulation of the conditional extremum problem and the solution procedure using the method of lagrange multipliers are explained. also, verification of obtained critical points and determination of the type of extremum are investigated.

14. 14.
    Setting the problem of optimal control in processes described by ordinary differential equations. .Lecture

    In the subject, the mathematical formulation of the problem of optimal control in dynamic processes described by ordinary differential equations is studied. control function, state variables, objective function and constraint conditions are explained. also, the areas of application of the optimal management problem and the main principles of the solution are investigated.

15. 15.
    Setting the problem of optimal control in processes described by ordinary differential equations.Lecture

    The subject studies the mathematical model of the problem of optimal control for dynamic processes described by ordinary differential equations. state variables, control function, initial and final conditions, and objective function are explained. also, the areas of application of optimal management and the main approaches leading to the solution of the problem are investigated.

1. K.q. hasanov, h.f. guliyev, m.h. yagubov, sh.sh. yusubov, "optimization methods", azerbaijan-2016/2017(opens in a new tab)
2. K.q. hasanov, h.f. guliyev, m.h. yagubov, sh.sh. yusubov, "optimization methods", azerbaijan-2016/2017(opens in a new tab)
3. Mokhtar s. bazaraa, john j. jarvis, hanif d. sherali, "linear programming and network flows", usa-2010(opens in a new tab)