Lectures related to Optimization with Constraints: KKT Conditions Explained

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

Optimisation in Energy Systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Optimization Programs: Piecewise Linear Cost Functions

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Linear Optimization Techniques: Problem Solving Approaches

Provides an overview of linear optimization techniques, focusing on problem-solving methods and the importance of constraints and objective functions.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Optimization Techniques: Stochastic Gradient Descent and Beyond

Discusses optimization techniques in machine learning, focusing on stochastic gradient descent and its applications in constrained and non-convex problems.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Optimization Methods: Lagrange Multipliers

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Introduction to Optimization

Introduces linear algebra, calculus, and optimization basics in Euclidean spaces, emphasizing the power of optimization as a modeling tool.

Deep Learning Building Blocks

Covers tensors, loss functions, autograd, and convolutional layers in deep learning.

Gradient Descent: Optimization and Constraints

Discusses gradient descent for optimization with equality constraints and iterative convergence criteria.

Optimization: Constrained Volume Problems

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Linear Algebra: Efficiency and Complexity

Explores constraints, efficiency, and complexity in linear algebra, emphasizing convexity and worst-case complexity in algorithm analysis.

Quasi-newton optimization

Covers gradient line search methods and optimization techniques with an emphasis on Wolfe conditions and positive definiteness.

Constraint Satisfaction: Formulation and Algorithms

Covers the formulation of constraint satisfaction problems and systematic algorithms for solving them efficiently.