Convexifying Nonconvex Problems: SDP and SOCP Relaxations

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

Optimal Decision Making: Sensitivity Analysis

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

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.

Approximation Algorithms

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

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Duality: Economic Interpretation

Explores duality in linear programming, strong duality, complementary slackness, and the economic interpretation of dual variables as prices.

Energy System Modeling: Optimization and Performance Indicators

Explores energy system modeling using optimization techniques and performance indicators.

Lagrangian Duality: Theory and Applications

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

Convex Optimization Problems: Theory and Applications

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