Algorithms_ITMO

Task 1. Experimental time complexity analysis

Goal

Experimental study of the time complexity of different algorithms.

Task 2. Algorithms for unconstrained nonlinear optimization. Direct methods

Goal

The use of direct methods (one-dimensional methods of exhaustive search, dichotomy, golden section search; multidimensional methods of exhaustive search, Gauss (coordinate descent), Nelder-Mead) in the tasks of unconstrained nonlinear optimization.

Task 3. Algorithms for unconstrained nonlinear optimization. First- and second-order methods

Goal

The use of first- and second-order methods (Gradient Descent, Non-linear Conjugate Gradient Descent, Newton’s method and Levenberg-Marquardt algorithm) in the tasks of unconstrained nonlinear optimization.

Task 4. Algorithms for unconstrained nonlinear optimization. Stochastic and metaheuristic algorithms

Goal

The use of stochastic and metaheuristic algorithms (Simulated Annealing, Differential Evolution, Particle Swarm Optimization) in the tasks of unconstrained nonlinear optimization and the experimental comparison of them with Nelder-Mead and Levenberg-Marquardt algorithms.

Task 5. Algorithms on graphs. Introduction to graphs and basic algorithms on graphs

Goal

The use of different representations of graphs and basic algorithms on graphs (Depth-first search and Breadth-first search).

Task 6. Algorithms on graphs. Path search algorithms on weighted graphs

Goal

The use of path search algorithms on weighted graphs (Dijkstra's, A* and Bellman-Ford algorithms).

Task 7. Algorithms on graphs. Tools for network analysis

Goal

The use of the network analysis software Gephi.

Task 8 (Extended). Practical analysis of advanced algorithms

Goal

Practical analysis of advanced algorithms.