Lecture

Branch and Bound: Optimization Techniques

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Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Explores the cutset formulation for the MST Problem and Gomory Cutting Planes method.

Covers the Branch & Bound algorithm for efficient exploration of feasible solutions and discusses LP relaxation, portfolio optimization, Nonlinear Programming, and various optimization problems.

Optimization Methods: Theory Discussion

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

Linear Programming: Weighted Bipartite Matching

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

Branch and Bound: Heuristic Maximization

Explains the Branch and Bound algorithm for heuristic maximization problems using LP relaxations and pruning techniques.

Linear Programming Basics

Covers deriving basic linear program representation, finding solutions, and exploring optimality.

Exact methods: Branch and Bound

Explores the Branch and Bound algorithm in discrete optimization, efficiently finding optimal solutions by calculating lower bounds on subsets.

Optimal Decision Making: Integer Programming

Covers integer programming, convex hulls, Gomory cutting planes, and branch and bound methods.

Discrete Optimization: Relaxation

Explores solving discrete optimization problems by relaxing integrality constraints.

Energy System Modeling: Optimization and Performance Indicators

Explores energy system modeling using optimization techniques and performance indicators.

Branch & Bound Algorithm: LP Based Approach

Explores the LP-based Branch & Bound algorithm for finding optimal solutions.

Simplex Algorithm: Basics

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Hedging for LPs

Covers the concept of hedging for Linear Programs and the simplex method, focusing on minimizing costs and finding optimal solutions.

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Solving Integer Linear Programs

Covers solving integer linear programs graphically, algorithmically, and through optimization methods.

Simplex Algorithm: Solution on a Vertex

Explores the simplex algorithm and how optimal solutions can be found on vertices of constraint polyhedra.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Optimisation Problem: Solving by FM

Covers the modelling and optimization of energy systems, focusing on solving optimization problems with constraints and variables.