Optimisation is one of today's most interesting fields of research in all areas of applied mathematics and engineering. In the field of scientific and technical computation, various equations which describe realistic problems like natural phenomena, or engineering problems such as cryptography, natural language processing, MRI reconstruction, wireless sensor networks, intrusion detection systems, financial portfolios, economic modelling, or uncertainty problems, can often be reduced to solving an optimisation problem. However, some of the aforementioned problems, particularly in various challenging real-world scenarios, are very difficult to solve using a mathematical analysis approach and must be solved numerically. In this case, numerical optimisation has become one of the most promising tools for different applications and has rapidly spread into many other disciplines.

Along with the development of basic optimisation algorithms, in the last several decades there is a trend in the scientific community to solve complex and global optimisation problems by using metaheuristic algorithms, such as genetic and swarm-intelligence optimisation algorithms. These algorithms use some randomness and imitate the evolution process in nature to avoid local optima. Traditional numerical algorithms aim to solve static optimisation problems which do not change in time. On the other hand, the dynamical approach in time-varying optimisation has several potential advantages, such as self-adaptation, parallel processing, and convenience for hardware implementation.

This Special Issue aims to portray an overview of recent research trends on this matter, with results opening pathways for future work. This Special Issue encourages original research papers of high quality that focus on new and recent developments in methodologies, techniques, and applications of numerical optimisation for solving various practical problems. In addition to original research, we also welcome review articles.

Potential topics include but are not limited to the following:

• Approximation and complexity in numerical optimisation
• Constrained and unconstrained optimisation
• Numerical PDE-constrained optimisation
• Linear and nonlinear complementarity problems
• Fuzzy optimisation
• Data envelopment analysis
• Global optimisation
• Metaheuristic algorithms
• Time-varying nonlinear optimisation
• Intelligent decision making
• Neural networks
• Deep learning algorithms