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About 3,196 papers for “Sequential quadratic programming”

Sequential Quadratic Programming

Paul T. Boggs, Jon W. Tolle · Acta Numerica · 1995

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

Cited by 1,776

REGULARIZED SEQUENTIAL QUADRATIC PROGRAMMING METHODS

Philip E. Gill, et al. · 2011

We present the formulation and analysis of a new sequential quadratic programming (SQP) method for general nonlinearly constrained optimization. The method pairs a primal-dual generalized augmented Lagrangian merit function with a flexible line search to obtain a sequence of improving estimates of the solution. This function is a primal-dual variant of the augmented Lagrangian proposed by Hestenes and Powell in the early 1970s. A crucial feature of the method is that the QP subproblems are convex, but formed from the exact second derivatives of the original problem. This is in contrast to methods that use a less accurate quasi-Newton approximation. Additional benefits of this approach include the following: (i) each QP subproblem is regularized; (ii) the QP subproblem always has a known feasible point; and (iii) a projected gradient method may be used to identify the QP active set when far from the solution.

Cited by 0

15. Sequential Quadratic Programming Methods

Society for Industrial and Applied Mathematics eBooks · 2000

15.1 Introduction At last, we turn to probably the most powerful, highly regarded methods for solving smooth nonconvex, nonlinear optimization problems involving nonlinear constraints, sequential quadratic programming (SQP)—or, as they are sometimes called, successive or recursive quadratic programming (RQP)—methods. As the names imply, such methods solve a sequence of quadratic programs. But, which quadratic programs? And why? The key to this is, as always, Newton's method. The goal is to produce rapidly convergent methods for the problem at hand. But in all of our haste, it is important not to forget to consider how best to embed these methods within a globally convergent framework. It is this issue that is particularly delicate. Rather than sneaking up on the solution in a rather indirect way, as do barrier methods (see Chapter 13) or differentiable penalty methods (see Chapter 14), SQP methods aim directly for a first-order critical point of the given nonlinear program minimizeƒ (x) subject to ci (x)=0 for i∈ℰ and ci (x)≥0 for i∈I. 15.1.1 Here, as before, ℰ and I are, respectively, disjoint sets of the indices of equality and inequality constraints, while ƒ and the smoothly map into ℝ. We start our exposition by, once again, considering the simplified problem minimizeƒ (x) subject to ci (x)=0 for i∈ℰ, 15.1.2 which only involves equality constraints, as it is here that the quadratic programming connection is most pronounced. Only then can we make the slightly tenuous connection with the general problem (15.1.1).

Cited by 2

3.2 Sequential Quadratic Programming.......................... 7

Jens Schreiber, Reviewer Prof, Dr. Kurt Geihs et al. · 2012

Optimization is present in fields such as Physics, Statistics, Data-Mining and Robotics. The optimization of continuous non-linear problems is here motivated by the field of Robotics, more precisely by IMPERA, – Integrated Mission Planning for Distributed Systems and the Middle Size League (MSL) of the RoboCup initiative. In this paper, we compare different solvers such as ALICA-Solver [7], Covariance Matrix Adaption Evolution Strategy (CMAES)[2], Sequential Quadratic Programming (SQP)[5] and two Hybrid-Solvers with a Hyper–redundant manipulator model [5]. We are especially interested in the comparison of ALICA-Solver to other solvers. Therefore we model a robot arm, which tries to grab an object and avoids obstacles as a typical task in the robotic domain. We show that ALICA-Solver is precise enough and as good as CMAES with respect to the median error. Furthermore, we can summarize that the ALICA-Solver has the fastest execution time and smallest amount of function evaluations in this benchmark problem.

Cited by 0

GPU Accelerated Sequential Quadratic Programming

Xiukun Hu, Craig C. Douglas, Robert Lumley et al. · 2017

Nonlinear optimization problems arise in all industries. Accelerating optimization solvers is desirable. Efforts have been made to accelerate interior point methods for large scale problems. However, since the interior point algorithm used requires many function evaluations, the acceleration of the algorithm becomes less beneficial. We introduce a way to accelerate the sequential quadratic programming method, which is characterized by minimizing function evaluations, on graphical processing units.

Cited by 7

Sequential Quadratic Programming Algorithms for Optimization

Francisco Javier García Prieto · 1989

Abstract : The problem considered in this dissertation is that of finding local minimizers for a function subject to general nonlinear inequality constraints, when first and perhaps second derivatives are available. The methods studies belong to the class on the SQP algorithm embodied in the code NPSOL, which was developed at the Systems Optimization Laboratory, Stanford University. The goal of the dissertation is to develop SQP algorithms that allow some flexibility in their design. Specifically, we are interested in introducing modifications that enable the algorithms to solve large-scale problems efficiently. The following issues are considered in detail: Instead of trying to obtain the search direction as a minimizer for the QP, the solution process is terminated after a limited number of iterations. Suitable termination criteria are defined that ensure convergence for an algorithm that use a quasi-Newton approximation for the full Hessian. Theorems concerning the rate of convergence are also given. For many problems the reduced Hessian is considerably smaller than the full Hessian. Consequently, there are considerable practical benefits to be gained by only requiring an approximation to the reduced Hessian. Theorems are proved concerning the convergence and rate of convergence for an algorithm that uses a quasi-Newton approximation for the reduced Hessian when early termination of the QP subproblem is enforced.

Cited by 10

Large-scale sequential quadratic programming algorithms

S.K. Eldersveld · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1992

The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

Cited by 13Open access

Sequential quadratic programming algorithms for optimization

Francisco J. Prieto · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1989

The problem considered is that of finding local minimizers for a function subject to general nonlinear inequality constraints, when first and perhaps second derivatives are available. The methods studied belong to the class of sequential quadratic programming (SQP) algorithms. In particular, the methods are based on the SQP algorithm embodied in the code NPSOL, which was developed at the Systems Optimization Laboratory, Stanford University. The goal of this paper is to develop SQP algorithms that allow some flexibility in their design. Specifically, we are interested in introducing modifications that enable the algorithms to solve large-scale problems efficiently. The following issues are considered in detail: instead of trying to obtain the search direction as a minimizer for the QP, the solution process is terminated after a limited number of iterations. Suitable termination criteria are defined that ensure convergence for an algorithm that uses a quasi-Newton approximation for the full Hessian. For many problems the reduced Hessian is considerably smaller than the full Hessian. Consequently, there are considerable practical benefits to be gained by only requiring an approximation to the reduced Hessian. Theorems are proved concerning the convergence and rate of convergence for an algorithm that uses a quasi-Newton approximation for the reduced Hessian when early termination of the QP subproblem is enforced. The use of second derivatives, while having significant practical advantages, introduces new difficulties; for example, the QP subproblems may be non-convex, and even a minimizer for the subproblem is no longer guaranteed to yield a suitable search direction. Also, theorems are proved for the convergence and rate of convergence of these algorithms. Finally, some numerical results, obtained from a modification of the code NPSOL, are presented. 43 refs., 4 tabs.

Cited by 5Open access