SNOPT: An SQP algorithm for large-scale constrained optimization
SNOPT: An SQP algorithm for large-scale constrained optimization
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DOI：
10.1137/s1052623499350013
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发表时间：
2002-04-26
影响因子：
3.1
通讯作者：
Saunders, MA
中科院分区：
文献类型：
--
作者：
Gill, PE;Murray, W;Saunders, MA
序列二次规划 (SQP) 方法已被证明对于解决目标和约束中具有平滑非线性函数的约束优化问题非常有效。在这里，我们考虑一般不等式约束（线性和非线性）的问题。我们假设一阶导数可用并且约束梯度是稀疏的。我们讨论了一种 SQP 算法，该算法使用平滑的增强拉格朗日评价函数，并明确规定了原始问题和 QP 子问题的不可行性。 SNOPT 是一种使用半定 QP 求解器的特殊实现。它基于拉格朗日 Hessian 的有限内存拟牛顿近似，并使用简化 Hessian 算法 (SQOPT) 来求解 QP 子问题。它专为解决具有数千个约束和变量但自由度适中（例如最多 2000 个）的问题而设计。一个重要的应用是航空航天工业中的轨迹优化。 CUTE 和 COPS 测试集中的大多数问题都给出了数值结果（大约 900 个示例）。
Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints ( linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse.We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom ( say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections ( about 900 examples).