Advanced Optimization (QEM)

The course presents the key optimization techniques used in modern theoretical economics, such as the Karush-Kuhn-Tucker method used to find extrema of constrained static problems or dynamic programming used to find optimal time paths of variables in a dynamic setup. The course provides the students with both theoretical and practical aspects of the techniques.

The goal of this course is to present the key optimization techniques used in modern theoretical economics. The course provides the students with both theoretical and practical aspects of the techniques, from general theorems on existence and uniqueness of extrema in certain important classes of problems, to applications of Lagrange, Karush-Kuhn-Tucker, and dynamic programming methods in typical economic problems. The course comprises both lectures and problem sessions. Students are required to be familiar with advanced calculus of real variables.

Literatura podstawowa:

1. A. de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press;

2. Course materials distributed in class

Literatura uzupełniająca:

1. K.Sydseater, P.Hammond, A.Seierstad, A.Strom, Further mathematics for economic analysis, Prentice Hall, 2008;

2. W.H.Fleming, R.W.Rishel, Deterministic and stochastic optimal control, Springer, 1975.

Evaluation criteria

Traditional Written Exam (3-4 problem tasks): 40.00%

Multiple Choice Test: 0.00%

Oral Exam: 0.00%

Test (3-4 problem tasks): 30.00%

Papers/Essays: 0.00%

Other (Homework and active participation in classes.): 30.00%

The threshold percentage of absences (excluding lectures)

defined as the proportion of class hours beyond which the achievement of learning outcomes is deemed unattainable: 50%

The course presents the key optimization techniques used in modern theoretical economics, such as the Karush-Kuhn-Tucker method used to find extrema of constrained static problems or dynamic programming used to find optimal time paths of variables in a dynamic setup. The course provides the students with both theoretical and practical aspects of the techniques.

The goal of this course is to present the key optimization techniques used in modern theoretical economics. The course provides the students with both theoretical and practical aspects of the techniques, from general theorems on existence and uniqueness of extrema in certain important classes of problems, to applications of Lagrange, Karush-Kuhn-Tucker, and dynamic programming methods in typical economic problems. The course comprises both lectures and problem sessions. Students are required to be familiar with advanced calculus of real variables.

Literatura podstawowa:

1. A. de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press;

2. Course materials distributed in class

Literatura uzupełniająca:

1. K.Sydseater, P.Hammond, A.Seierstad, A.Strom, Further mathematics for economic analysis, Prentice Hall, 2008;

2. W.H.Fleming, R.W.Rishel, Deterministic and stochastic optimal control, Springer, 1975.

Evaluation criteria

Traditional Written Exam (3-4 problem tasks): 40.00%

Multiple Choice Test: 0.00%

Oral Exam: 0.00%

Test (3-4 problem tasks): 30.00%

Papers/Essays: 0.00%

Other (Homework and active participation in classes.): 30.00%

The threshold percentage of absences (excluding lectures)

defined as the proportion of class hours beyond which the achievement of learning outcomes is deemed unattainable: 50%

The course presents the key optimization techniques used in modern theoretical economics, such as the Karush-Kuhn-Tucker method used to find extrema of constrained static problems or dynamic programming used to find optimal time paths of variables in a dynamic setup. The course provides the students with both theoretical and practical aspects of the techniques.

The goal of this course is to present the key optimization techniques used in modern theoretical economics. The course provides the students with both theoretical and practical aspects of the techniques, from general theorems on existence and uniqueness of extrema in certain important classes of problems, to applications of Lagrange, Karush-Kuhn-Tucker, and dynamic programming methods in typical economic problems. The course comprises both lectures and problem sessions. Students are required to be familiar with advanced calculus of real variables.

Literatura podstawowa:

1. A. de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press;

2. Course materials distributed in class

Literatura uzupełniająca:

1. K.Sydseater, P.Hammond, A.Seierstad, A.Strom, Further mathematics for economic analysis, Prentice Hall, 2008;

2. W.H.Fleming, R.W.Rishel, Deterministic and stochastic optimal control, Springer, 1975.

Evaluation criteria

Traditional Written Exam (3-4 problem tasks): 40.00%

Multiple Choice Test: 0.00%

Oral Exam: 0.00%

Test (3-4 problem tasks): 30.00%

Papers/Essays: 0.00%

Other (Homework and active participation in classes.): 30.00%

The threshold percentage of absences (excluding lectures)

defined as the proportion of class hours beyond which the achievement of learning outcomes is deemed unattainable: 50%

The course presents the key optimization techniques used in modern theoretical economics, such as the Karush-Kuhn-Tucker method used to find extrema of constrained static problems or dynamic programming used to find optimal time paths of variables in a dynamic setup. The course provides the students with both theoretical and practical aspects of the techniques.

The goal of this course is to present the key optimization techniques used in modern theoretical economics. The course provides the students with both theoretical and practical aspects of the techniques, from general theorems on existence and uniqueness of extrema in certain important classes of problems, to applications of Lagrange, Karush-Kuhn-Tucker, and dynamic programming methods in typical economic problems. The course comprises both lectures and problem sessions. Students are required to be familiar with advanced calculus of real variables.

Literatura podstawowa:

1. A. de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press;

2. Course materials distributed in class

Literatura uzupełniająca:

1. K.Sydseater, P.Hammond, A.Seierstad, A.Strom, Further mathematics for economic analysis, Prentice Hall, 2008;

2. W.H.Fleming, R.W.Rishel, Deterministic and stochastic optimal control, Springer, 1975.

The course presents the key optimization techniques used in modern theoretical economics, such as the Karush-Kuhn-Tucker method used to find extrema of constrained static problems or dynamic programming used to find optimal time paths of variables in a dynamic setup. The course provides the students with both theoretical and practical aspects of the techniques.

The goal of this course is to present the key optimization techniques used in modern theoretical economics. The course provides the students with both theoretical and practical aspects of the techniques, from general theorems on existence and uniqueness of extrema in certain important classes of problems, to applications of Lagrange, Karush-Kuhn-Tucker, and dynamic programming methods in typical economic problems. The course comprises both lectures and problem sessions. Students are required to be familiar with advanced calculus of real variables.

Literatura podstawowa:

1. A. de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press;

2. Course materials distributed in class

Literatura uzupełniająca:

1. K.Sydseater, P.Hammond, A.Seierstad, A.Strom, Further mathematics for economic analysis, Prentice Hall, 2008;

2. W.H.Fleming, R.W.Rishel, Deterministic and stochastic optimal control, Springer, 1975.