Interior-point methods have been a re-emerging field in optimization since the mid-1980s. We will present here ways of improving the performance of these algorithms for nonlinear optimization and extending them to different classes of problems and application areas.; At each iteration, an interior-point algorithm computes a direction in which to proceed, and then must decide how long of a step to take. The traditional approach to choosing a steplength is to use a merit function, which balances the goals of improving the objective function and satisfying the constraints. Recently, Fletcher and Leyffer reported success with using a filter method, where improvement of any of the objective function and constraint infeasibility is sufficient. We have combined these two approaches and applied them to interior-point methods for the first time and with good results.; Another issue in nonlinear optimization is the emergence of several popular problem classes and their specialized solution algorithms. Two such problem classes are Second-Order Cone Programming (SOCP) and Semidefinite Programming (SDP). In the second part of this dissertation, we show that problems from both of these classes can be reformulated as smooth convex optimization problems and solved using a general purpose interior-point algorithm for nonlinear optimization.
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