The 2015 World Congress on Global Optimization (WCGO IV) took place during February 22–25, 2015 in Gainesville, Florida, USA. This congress offered an excellent forum for researchers and practitioners in the field of global optimization from all over the world.

A primary goal of the congress was to bring together scientists, engineers, mathematicians and participants from a variety of related disciplines, to exchange ideas and present original research results in the theory and applications of global optimization. This goal was achieved to a great extent.

The congress was organized by the International Society of Global Optimization, the Center for Applied Optimization, and the Department of Industrial and Systems Engineering at the University of Florida.

A major event during the congress was the Carathéodory Prize award ceremony. The Constantin Carathéodory Prize of the International Society of Global Optimization is awarded bi-annually to an individual (or a group) for fundamental contributions to theory, algorithms, and applications of global optimization. The Prize is awarded for outstanding work that reflects contributions that have stood the test of time. The criteria include scientific excellence, innovation, significance, depth, and impact.

Christodoulos A. Floudas of Texas A&M University, Ignacio E. Grossmann of Carnegie Mellon University, and Nikolaos Sahinidis, also of Carnegie Mellon University have been awarded the Constantin Carathéodory Prize of the International Society of Global Optimization in recognition of their lifetime contributions to global optimization, and in particular the development of global optimization software.

This special issue of Journal of Global Optimization contains selected refereed papers presented at the 2015 World Congress on Global Optimization. The first three papers are based on the lectures of the Constantin Carathéodory Prize winners.

I would like to take this opportunity to thank all authors and referees for their patience and excellent work during the editing process of this special issue. The collection of papers in this issue reflects the progress in global optimization and the interdisciplinary nature of the field.