Modern optimisation theory and associated methods have seen significant and rapid progress in recent decades. These advances have had an important impact on the development of many areas of science, engineering, and technology, as well as business and finance. One of the areas of optimisation that has had the strongest development both in theory and methods is the area of convex conic optimisation. There are three major factors that have contributed to such development. The first is the fact that convex conic optimisation is a unifying frame that contains important optimisation problems, such as linear optimisation, second-order cone optimisation, and semidefinite optimisation as special cases. In addition, convex conic optimisation has combined Euclidean Jordan algebras and related symmetric cones with optimisation theory leading to strong and significant research results, and a still very active research area. The second factor is the fact that interior-point methods, which have in many ways revolutionized the theory and methods of mathematical programming, have shown to be efficient algorithms in solving conic optimisation problems, both theoretically and practically. The third factor is the numerous applications in various fields, such as statistics, optimal experiment design, information and communication theory, electrical engineering, portfolio optimisation, and combinatorial optimisation, that can be formulated as conic optimisation problems and solved efficiently using appropriate interior-point methods.

The need to solve challenging large-scale optimisation problems arising in various areas of science, engineering, and technology has led to breakthrough advancements in numerical optimisation, including first-order methods and augmented Lagrangian methods. These and other optimisation methods have contributed to rapid development in many fields, including operations research, data science, data analytics, machine learning, and artificial intelligence, among many others. Significant progress has also been made in solving difficult and previously non-tractable problems such as non-convex and/or non-symmetric optimisation, nonlinear conic optimisation, sparse optimisation, and stochastic optimisation problems with applications in science and engineering. However, many challenges and open questions still remain as the size of problems and the need to solve them efficiently is increasing.

The aim of this Special Issue is to provide a comprehensive collection of cutting-edge research contributions on optimisation theory, methods, and applications in science and engineering. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Optimisation Theory
• Linear and Nonlinear Optimisation
• Interior-Point Methods and Related Topics
• First-Order Methods and Related Topics
• Sparse Optimisation
• Robust Optimisation
• Stochastic Optimisation
• Conic Optimisation
• Complementarity Problems and Variational Inequalities
• Discrete and Combinatorial Optimisation
• Applications of optimisation theory and methods