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求多变量非线性方程 F(x) = 0 的解。您也可以使用基于问题的方法求解标量方程或线性方程组,或由 F(x) = G(x) 表示的方程组(等效于使用基于求解器的方法求解 F(x) – G(x) = 0)。对于非线性方程组,求解器将方程求解问题转换为最小化 F 的分量平方和的优化问题,即 min(∑Fi2(x))。线性方程和标量方程有不同的求解算法;请参阅方程求解算法。
在开始求解优化问题之前,您必须选择合适的方法:基于问题或基于求解器。有关详细信息,请参阅 首先选择基于问题或基于求解器的方法。
对于基于问题的方法,请创建问题变量,然后用这些变量表示方程。有关基于问题的求解步骤,请参阅Problem-Based Workflow for Solving Equations。要求解生成的问题,请使用 solve
。
有关基于求解器的求解步骤,包括定义目标函数和选择合适的求解器,请参阅基于求解器的优化问题设置。
EquationProblem | System of nonlinear equations |
OptimizationEquality | Equalities and equality constraints |
OptimizationExpression | Arithmetic or functional expression in terms of optimization variables |
OptimizationVariable | Variable for optimization |
Solve Nonlinear System of Equations, Problem-Based
Solve a system of nonlinear equations using the problem-based approach.
Solve Nonlinear System of Polynomials, Problem-Based
Solve a polynomial system of equations using the problem-based approach.
Follow Equation Solution as a Parameter Changes
Solve a sequence of problems using the previous solution as a start point.
Nonlinear System of Equations with Constraints, Problem-Based
Solve a system of nonlinear equations with constraints using the problem-based approach.
Solve Nonlinear System Without and Including Jacobian
Use derivatives in nonlinear equation solving.
Large System of Nonlinear Equations with Jacobian Sparsity Pattern
Solve a nonlinear system of equations with a known finite-difference sparsity pattern.
了解求解具有约束的非线性方程组的方法。
What Is Parallel Computing in Optimization Toolbox?
Use multiple processors for optimization.
Using Parallel Computing in Optimization Toolbox
Perform gradient estimation in parallel.
Improving Performance with Parallel Computing
Investigate factors for speeding optimizations.