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This repository includes all the assignments, the slides, and the final project of the Convex Optimization II graduate course.
convexoptimization2's Introduction
ConvexOptimization2, Graduate course
This repository includes all the assignments, the slides, and the final project of the Convex Optimization II graduate course.
- HW1: Linear Programming, Integer Programming
- HW2: KKT Conditions, Convex/Concave Problems, Lagrangian & Dual Problem
- HW3: Matlab CVX, Solve Convex Problem (By Dual Problem), Strong Duality
- HW4: Scheduling, Stochastic Optimization
- Project: Multi-Objective Portfolio Optimization
This course contains the following topics:
- Combinatorial Optimization:
- Linear programming and its applications (Multi-commodity flow problem)
- Mixed integer programming
- Approximation algorithms (LP relaxation, rounding methods)
- Set cover and Knapsack problem analysis
- Convex analysis and optimization
- Convex set and convex functions
- Convex optimization
- Lagrange dual problem, KKT optimality conditions
- Gradient and subgradient methods to solve convex optimization problems
- Decomposition methods and distributed optimization:
- Dual decomposition
- Primal decomposition
- Indirect decomposition
- Hierarchical decomposition
- Applications and use cases
- Optimization in communication networks :
- Transmission Control Protocol (TCP)- Optimization-based congestion control
- Fairness in Resource Allocation Problems
- Generalized Network Utility Maximization
- Stochastic and robust optimization:
- Optimization under uncertainty
- Risk averse optimization
- Optimization of infinite horizon time
- Lyapunov optimization
- Applications and use cases (Newsvendor problem, stock market analysis, stochastic networks, stable scheduling)
- Non-convex problems:
- Regularization and Convexification
- Convex-Cardinality Problems
- Sequential convex programming
- Applications and use cases (learning, data fitting)
- Bandit Convex Optimization:
- Applications in machine learning
- Large-scale optimization.
- Alternating direction method of multipliers (ADMM)
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