Kiyohiro Ikeda is Professor Emeritus at Tohoku University, Japan. His research interests include the application of bifurcation theory to bifurcation and buckling in structures and materials, as well as the theoretical and numerical analysis of structures with initial imperfections. Kazuo Murota is a Project Professor at the Institute of Statistical Mathematics, Japan, as well as Professor Emeritus at the University of Tokyo, Kyoto University, and Tokyo Metropolitan University, Japan. His research interests include bifurcation theory, discrete optimization, and numerical analysis.