Fundamental theoretical concepts of static convex and non-convex programming. First and second order optimality conditions for analytical solution of single-variable constrained and unconstrained optimization. Optimality conditions for analytical solution of multivariable optimization problems with constrants. Linear programming. Numerical solution of single-variable problems. Numerical solution of multi-variable problems, with and without constraints. Fundamentals of variational calculus. Optimal control: Pontryagin maximum principle. Numerical methods of dynamic programming. Modern search strategies: Evolutionary & Genetic optimization, Particle Swarm Optimization. Optimization techniques in neural networks training and in fuzzy systems design. Applications in real-life engineering problems, including, but not limited to, identification of nonlinear biological and medical models. Application in biomedical engineering.