“sequential quadratic programming”的概念、定义、翻译、参考文献-科学参考

sequential quadratic programming

Computer

A widely used and successful approach to solving constrained optimization problems, that is
$minimize F (x), x = {(x_{1}, x_{2}, \dots, x_{n})}^{T},$
where F(x) is a given objective function of n real variables, subject to the t nonlinear constraints on the variables,
$c_{i} (x) = 0, i = 1, 2, \dots, t$
Inequality constraints are also possible. A solution of this problem is also a stationary point (a point at which all the partial derivatives vanish) of the related function of x and λ‎,
$\begin{array}{l} L (x, λ) = F (x) - Σ λ_{i} c_{i} (x), \\ λ = (λ_{1}, λ_{2}, \dots, λ_{t}) \end{array}$
A quadratic approximation to this function is now constructed that along with linearized constraints forms a quadratic programming problem – i.e., the minimization of a function quadratic in the variables, subject to linear constraints. The solution of the original optimization problem, say x*, is now obtained from an initial estimate and solving a sequence of updated quadratic programs; the solutions of these provide improved approximations, which under certain conditions converge to x*.

单词	sequential quadratic programming
释义	sequential quadratic programming Computer A widely used and successful approach to solving constrained optimization problems, that is $minimize F (x), x = {(x_{1}, x_{2}, \dots, x_{n})}^{T},$ where F(x) is a given objective function of n real variables, subject to the t nonlinear constraints on the variables, $c_{i} (x) = 0, i = 1, 2, \dots, t$ Inequality constraints are also possible. A solution of this problem is also a stationary point (a point at which all the partial derivatives vanish) of the related function of x and λ‎, $\begin{array}{l} L (x, λ) = F (x) - Σ λ_{i} c_{i} (x), \\ λ = (λ_{1}, λ_{2}, \dots, λ_{t}) \end{array}$ A quadratic approximation to this function is now constructed that along with linearized constraints forms a quadratic programming problem – i.e., the minimization of a function quadratic in the variables, subject to linear constraints. The solution of the original optimization problem, say x, is now obtained from an initial estimate and solving a sequence of updated quadratic programs; the solutions of these provide improved approximations, which under certain conditions converge to x.
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