Introduction: fundamentals of numerical analysis; setting and division of optimization problems and methods for their solution; basic steps of optimization problem solutions. Fundamentals of numerical analysis: functions, matrix algebra. System of linear algebraic equations: Theorems, transformations of equivalence; permutation matrices; solving solutions (Gauss's elimination process, triangular decomposition) and optimal equation ordering (Quasi-optimal methods and Tunney optimal schemes). Space matrices techniques: static and dynamic storage schemes. Matrix inversion: classical methods and matrix inversion lemmas. System of nonlinear algebraic equations: iterative solution corrections; bracketing a root and combined methods; basic and modified Newton-Raphson methods; basic and accelerated Gauss-Seidel methods. Regression analysis: random values; data model; correlation; residual; WLS and linear regression. Fundamentals of problem optimization: variables, objective function, constraints, feasible region, direction vector, step size, mathematical model, graphical interpretation, transformation and characteristics. Optimization methods: convex optimization (convex set and function, extreme point, convex problem, optimal conditions, convex programming); linear optimization (standard and canonical forms, Simplex method, Interior-point method, methods with and without calculation of derivatives, network problem, transport problem, assignment problem); nonlinear optimization (necessary and sufficient conditions, methods with and without calculation of derivatives, quadratic programming, Lagrange multipliers method); integer/discrete optimization (linear and nonlinear problems; all-integer, mix integer and 0-1 problems; catting plane methods; branch and bounds methods ); dynamic optimization; multi-objective optimization (Trade-off, Pareto optimization).