Optimization Toolbox 6.0 - The MathWorks - #9

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Optimization Toolbox 6.0 table.main {} tr.row {} td.cell {} div.block {} div.paragraph {} .font0 { font:5.00pt "Arial", sans-serif; } .font1 { font:7.00pt "Arial", sans-serif; } .font2 { font:9.00pt "Arial", sans-serif; } .font3 { font:8.00pt "Times New Roman", serif; } .font4 { font:15.00pt "Times New Roman", serif; } Solving an n-dimensional Rosenbrock function using the nonlinear équation solver. Linear Programming Engineers and scientists use mathematical modeling to describe the behavior of Systems under study. System requirements, when defined mathematically as constraints on the decision variables input into the mathematical system model, form a mathematical program. This mathematical program, or optimization problem description, can then be solved using optimization techniques. Linear programming is one class of mathematical programs where the objective and constraints consist of linear relationships. Linear programming problems consist of a linear expression for the objective function and linear equality and inequality constraints. Optimization Toolbox includes three algorithms used to solve this type of problem: ■ The interior point algorithm is based on a primal-dual predictor-corrector algorithm used for solving linear programming problems. Interior point is especially useful for large-scale problems that have structure or can be defined using sparse matrices. ■ The active-set algorithm minimizes the objective at each iteration over the active set (a subset of the constraints that are locally active) until it reaches a solution. ■ The simplex algorithm is a systematic procedure for generating and testing candidate vertex solutions to a linear program. The simplex algorithm is the most widely used algorithm for linear programming. MathWorks- Accelerating the pace of engineering and science 9