Optimization

3 Credits · Level: Graduate, Undergraduate

Optimization problems arise in a variety of fields, such as the most economic transport of goods from service points to destinations, the design of components in manufacturing, or the desire to minimize noises and vibrations in airplanes or cars. The mathematical formulation of optimization problems results in the task to minimize or maximize functions which may be subject to additional conditions or constraints. Optimization problems arise in a variety of fields, such as the most economic transport of goods from service points to destinations, the design of components in manufacturing, or the desire to minimize noises and vibrations in airplanes or cars. The mathematical formulation of optimization problems results in the task to minimize or maximize functions which may be subject to additional conditions or constraints. Certain optimization problems, such as finding the extreme values (maxima and minima) of continuous functions of several variables, are already discussed in calculus. Of particular interest in this course are extreme value problems with constraints on the function, possibly given by additional equations, inequalities, or differential equations. According to the type and the nature of the constraint, different techniques of solving the optimization problem are to be developed. These include linear programming, nonlinear programming, variational problems, and optimal control. Students will see a good number of examples of optimization problems, study various analytical techniques of solving them, reinforce their knowledge of differential calculus of functions of several variables, and should gain an appreciation of two fundamental mathematical concepts: Linearity and Convexity. This course can be taken for graduate credit. Credits: 3 Prerequisites: Math-201 or equivalent. Certain optimization problems, such as finding the extreme values (maxima and minima) of continuous functions of several variables, are already discussed in calculus. Of particular interest in this course are extreme value problems with constraints on the function, possibly given by additional equations, inequalities, or differential equations. According to the type and the nature of the constraint, different techniques of solving the optimization problem are to be developed. These include linear programming, nonlinear programming, variational problems, and optimal control. Students will see a good number of examples of optimization problems, study various analytical techniques of solving them, reinforce their knowledge of differential calculus of functions of several variables, and should gain an appreciation of two fundamental mathematical concepts: Linearity and Convexity. This course can be taken for graduate credit. Credits: 3 Prerequisites: Math-201 or equivalent.