NUMERICAL COMPUTATION AND OPTIMISATION METHODS WITH MATLAB (ePub)

This book develops numerical computation and optimisation methods across examples an exercices. MATLAB can be used as a high-level programming language that includes data structures, functions, control-flow instructions, input/output handling and even object-oriented programming. MATLAB programming methods allow numerical computational techniques to be tackled through the simple implementation of theoretical algorithms that solve a wide range of problems (equations, systems, derivatives, integrals, differential equations,..). Among these problems, the solution of non-linear equations plays an important role. On the other hand, MATLAB Optimization Toolbox provides functions to search for parameters that minimise or maximise objectives while satisfying constraints. The toolbox includes solvers for linear programming (LP), mixed integer linear programming (MILP), quadratic programming (QP), second order cone programming (SOCP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares and nonlinear equations. You can define the optimisation problem with functions and matrices, or by specifying variable expressions that reflect the underlying mathematics. You can use automatic differentiation of objective and constrained functions to obtain faster and more accurate solutions. You can use the toolbox solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analysis, and incorporate optimisation methods into algorithms and applications. The toolbox allows you to perform design optimisation tasks, including parameter estimation, component selection and parameter tuning. It can be used to find optimal solutions in applications such as portfolio optimisation, energy management and trading, and production planning. Optimization Toolbox has two approaches to solving optimisation problems or equations: problem-based and solver-based. Before you start solving a problem, you must first choose the appropriate approach.