High Performance Computing (HPC) aims at providing reasonably fast computing solutions to both scientific and real life technical problems. Many efforts have indeed been made on the way to powerful supercomputers, both generic and customized configurations. However, whatever their current and future breathtaking capabilities, supercomputers work by brute force and deterministic steps, while human mind works by few strokes of brilliance. Thus, in order to take a significant advantage of hardware advances, we need powerful methods to solve problems together with highly skillful programming efforts and relevant frameworks. The advent of multicore architectures is noteworthy in the HPC history, because it has brought the underlying concept of multiprocessing into common consideration and has changed the landscape of standard computing. At a larger scale, there is a keen desire to build or host frontline supercomputers. The yearly Top500 ranking nicely illustrates and orchestrates this supercomputers saga. For many years, computers have been falling in price while gaining processing power often strengthened by specialized accelerator units. We clearly see that what commonly springs up in mind when it comes to HPC is computer capability. However, this availability of increasingly fast computers has changed the rule of scientific discovery and has motivated the consideration of challenging applications. Thus, we are routinely at the door of large-scale problems, and most of time, the speed of calculation by itself is no longer sufficient. Indeed, the real concern of HPC users is the time-to-output. Thus, we need to study each important aspect in the critical path between inputs and outputs, and keep striving to reach the expected level of performance. This is the main concern of the viewpoints and the achievements reported in this book. The document is organized into five chapters articulated around our main contributions. The first chapter depicts the landscape of supercomputers, comments the need for tremendous processing speed, and analyze the main trends in supercomputing. The second chapter deals with solving large-scale combinatorial problems through a mixture of continuous and discrete optimization methods, we describe the main generic approaches and present an important framework on which we have been working so far. The third chapter is devoted to the topic accelerated computing, we discuss the motivations and the issues, and we describe three case studies from our contributions. In chapter four, we address the topic of energy minimization in a formal way and present our method based on a mathematical programming approach. Chapter five debates on hybrid supercomputing, we discuss technical issues with hierarchical shared memories and illustrate hybrid coding through a large-scale linear algebra implementation on a supercomputer.
