Description: 1 Introduction.- 2 Duality.- 3 Polynomiality of Path-following Methods.- 4 Self-Dual Embedding Technique.- 5 Properties of the Central Path.- 6 Superlinear Convergence.- 7 Central Region Method.- 8 An Implementation of the Homogeneous Algorithm.- 9 A Simplified Correctness Proof for Interior Point Algorithm.- 10 New Analysis of Newton Methods for LCP.- 11 Numerical Evaluation of SDPA.- 12 Robust Modeling of Multi-Stage Portfolio Problems.- 13 An Interior Point SQP Parallel B&B Method.- 14 Solving Linear Ordering Problems.- 15 Finite Element Methods for Solving Parabolic Inverse Problems.- 16 Error Bounds For Quadratic Systems.- 17 Squared Functional Systems and Optimization Problems.- 18 Interior Point Methods: Current Status and Future Directions.

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