On Thursday, December 19th, at 2pm30 pm, the first lecture of the mini-course on optimization will be held at the INM RAS (room 727). The speaker of the course is Roland Hildebrand, Leading Researcher from MIPT. The course will consist of four lectures. The program of the course can be found below. All are welcome.
1. General Information
Examples of Problems
– Multicriteria Optimization
– Pareto Set
Heuristics and Optimal Solutions
Formalizing the Problem as an Optimization Problem
– The Form for Recording Optimization Tasks
– Classification of Optimization Problems
Task Classes
– Oracles
– Complexity of Problem Classes
– Convergence Criteria
Example: One-Dimensional Search, Dichotomy Solvers
– Computer Formats
2. Unstructured Optimization
Unconstrained optimization problems. Gradient descent method. Newton’s method. Automatic differentiation. Conjugate gradient method. Block coordinate descent.
Optimization with constraints. Lagrange multiplier method. Projected gradient method. Frank-Wolfe method. Barrier functions and penalty functions.
Applications in machine learning and decomposition of complex problems.
3. Structured Optimization
Linear Programming: Optimality Conditions, Strong Duality, The Simplex Method, the Inner Point Method, Sparsity
Semidefinite Programming: Applications
4. Discrete and Mixed-Integer Optimization:
Examples of tasks include backpacking, packaging, coloring, and matching. Heuristic approaches and relaxation techniques are used to solve these problems. The method of branches and bounds, as well as the randomized Gemans-Williams method, are two examples of techniques used in this field.
Pi / 2 Nesterov’s Theorem is also relevant to this topic.
For any organizational matters, please contact Natalia Zakharova, the Scientific Secretary of the Moscow Center of Fundamental and Applied Mathematics in the INM RAS.