Concept

Semidefinite programming

Related lectures (32)

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

Convex Optimization: Generalized Inequalities

Explores problems with generalized inequalities in convex optimization and the equivalence between SOCP and SDP.

Optimal Power Flow: Constraints and Relaxations

Covers the Optimal Power Flow problem in power systems, focusing on constraints and relaxation methods to efficiently solve the nonconvex QCQP.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Polynomial Optimization: SOS and SDP

Explores Sum of Squares polynomials and Semidefinite Programming in Polynomial Optimization, enabling the approximation of non-convex polynomials with convex SDP.

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

Semidefinite Programming: Formulations and Applications

Explores Semidefinite Programming formulations, SDP relaxations, and optimization strategies with convergence guarantees.

Convex Relaxation in Optimization

Explores convexifying nonconvex problems through relaxation techniques, illustrated with total variation reconstruction examples.

Optimisation with Constraints: Interior Point Algorithm

Explores optimization with constraints using KKT conditions and interior point algorithm on two examples of quadratic programming.

Linear Programming: Two-phase Simplex Algorithm

Covers the application of the two-phase Simplex algorithm to solve linear programming problems.

Convex Optimization Problems: Standard Form

Covers convex optimization problems, transformation to standard form, and optimality criteria for differentiable objectives.

Solving Integer Linear Programs

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

Convex Optimization: Duality and KKT Conditions

Explores convex optimization duality, KKT conditions, and financial arbitrage detection.

Discrete optimization: Knapsack

Explores modeling classic optimization problems as mixed integer linear problems, focusing on the knapsack problem and its applications.

Initial BFS

Explores finding the initial Basic Feasible Solution (BFS) in a linear program.

Trajectory Optimization with CALIPSO

Introduces CALIPSO, a solver for trajectory optimization with constraints in robotics, showcasing methods and examples.

Nonconvex Optimization: Challenges and Strategies

Explores nonconvex optimization challenges and strategies, including blind image deconvolution and SDP relaxations.

Convex Optimization Problems: Theory and Applications

Explores convex optimization problems, optimality criteria, equivalent problems, and practical applications in transportation and robotics.

Convex Optimization: Dual Cones

Explores dual cones, generalized inequalities, SDP duality, and KKT conditions in convex optimization.