Optimization Toolbox
Optimization Toolbox offers tools for determining parameters that either minimize or maximize objectives while meeting given constraints. It provides solvers for a variety of problems, including 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 systems of nonlinear equations.
Optimization problems can be formulated using functions and matrices or through variable-based expressions that capture the mathematical model. The toolbox also supports automatic differentiation of objective and constraint functions, enabling faster and more precise results.
With its solvers, you can address both continuous and discrete optimization tasks, conduct tradeoff studies, and embed optimization strategies into broader algorithms and applications. It supports design optimization processes such as parameter estimation, component selection, and parameter tuning. Practical applications include portfolio optimization, energy management and trading, and production scheduling.
Defining Optimization Problems
Model a design or decision problem as an optimization problem. Set design parameters and decisions as optimization variables. Use variables to define an objective function to optimize and use constraints to limit possible variable values.
Solving Optimization Problems
Apply a solver to the optimization problem to find an optimal solution: a set of optimization variable values that produce the optimal value of the objective function, if any, and meet the constraints, if any.
Nonlinear Programming
Solve optimization problems that have a nonlinear objective or are subject to nonlinear constraints.
Linear and Mixed-Integer Linear Programming
Solve optimization problems that have a linear objective subject to linear constraints with continuous and/or integer variables.
Quadratic and Conic Programming
Solve optimization problems with a quadratic objective and linear constraints or problems with second-order cone constraints.
Least Squares
Solve linear and nonlinear least-squares problems subject to bound, linear, and nonlinear constraints.
Systems of Nonlinear Equations
Solve systems of nonlinear equations subject to bound, linear, and nonlinear constraints.
Multiobjective Optimization
Solve optimization problems that have multiple objective functions subject to a set of constraints.
Deployment
Build optimization-based decision support and design tools, integrate with enterprise systems, and deploy optimization algorithms to embedded systems.
