This volume contains a selection of papers that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA from July 30-August 1, 2012. MOPTA 2012 brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. The goal was to host presentations on the exciting developments in different areas, and at the same time provide a setting for close interaction among the participants. The topics covered at MOPTA 2012 varied from algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The papers to be contained in the volume represent a sample of these topics and applications, and illustrate the broad diversity of ideas discussed at the conference. This volume is suitable for both graduate students as well as researchers in the field.