W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, Tech Report, Department of Operations Research, Stanford University, (1992).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....manifestation via the linear (preconditioned) conjugate gradient method, is one of the key ideas to have evolved in the unconstrained case during the 20th century. So it is clearly desirable to truncate the LP QP solution process. But how We are aware of almost no work in this area (but see [24] for an exception) and it is of vital practical importance. Again, it would seem easier to stop early with an active set QP solver than with an interiorpoint one. Finally, we would ultimately expect that the active sets for our LP QP subproblems will settle down as we approach the solution to ....

W. Murray and F. J. Prieto. A sequential quadratic programming algorithm using an incomplete solution of the subproblem. SIAM Journal on Optimization, 5(3):590{ 640, 1995.

....trust region globalizations requires techniques different from those that can be used for line search globalizations. Other papers which investigate SQP methods for large scale problems, but without treatment of inexact linear systems solves and inexact derivative information include [1] 31] [36]. This paper is organized as follows. In Section 2, we state the first order necessary optimality conditions of problem (1.1) A review of the features of the exact TRIP SQP algorithms necessary for the inexact analysis is given in Section 3. The inexact TRIP SQP algorithms are presented in ....

W. MURRAY AND F. J. PRmTO, A sequential quadraticprogramming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590 640.

....constraints are equalities. We should note, however, that the ideas presented here can be used within an active set method for inequality constrained optimization such as that implemented in the SNOPT code [16] For other work on reduced or full Hessian SQP methods for large scale optimization see [1, 3, 10, 22, 25, 27, 23, 15]. 2. The Implemented Algorithm The broad overview just given of the reduced Hessian algorithm does not include a description of various devices introduced in [2] to globalize the iteration and ensure a fast rate of convergence. Other aspects of the algorithm that were not reviewed include the ....

W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, Tech Report, Department of Operations Research, Stanford University, 1992.

....[15] a projected Lagrangian method originally developed for linear constraints. A more recent example is LANCELOT [9] which is an augmented Lagrangian method, employing an 1 norm trust region, with numerous options helpful in solving various classes of problems. Examples of SQP approaches include [14] and [12] Some algorithms provide the option of using interior point methods to solve for the descent direction (see, for example [11] while others involve various direct extensions of the interior point ideas to the nonlinear setting, including [10] Our approach differs significantly from ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM Journal on Optimization, 5 (1995), pp. 590--640. 30 P. T. BOGGS, A. J. KEARSLEY, AND J. W. TOLLE

....m k (s) f k hg k ; si 1 2 hs; H k si; 2.3) and where k Delta k denotes the Euclidean norm. Remarkably, most of the existing SQP algorithms assume that an exact local solution of QP(x k ) or TRQP(x k ; Delta k ) is found, although attempts have been made by Dembo and Tulowitzki (1983) and Murray and Prieto (1995) to design conditions under which an approximate solution of the subproblem is acceptable. We revisit this issue in what follows, and start by noting that the step s k may be viewed as the sum of two distinct components, a normal step n k , such that x k n k satisfies the constraints of TRQP(x k ....

W. Murray and F. J. Prieto. A sequential quadratic programming algorithm using an incomplete solution of the subproblem. SIAM Journal on Optimization, 5(3), 590-- 640, 1995.

....trust region globalizations requires techniques different from those that can be used for line search globalizations. Other papers which investigate SQP methods for large scale problems, but without treatment of inexact linear systems solves and inexact derivative information include [1] 31] [36]. This paper is organized as follows. In Section 2, we state the first order necessary optimality conditions of problem (1.1) A review of the features of the exact TRIP SQP algorithms necessary for the inexact analysis is given in Section 3. The inexact TRIP SQP algorithms are presented in ....

W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590--640.

....in which two Cauchy points are determined (see Sections 3.2, 3.3, and 3.6) or as a single step in which an auxiliary computational may be necessary (see Section 3. 1) As yet, the only method we are aware of that allows a direct truncation of the QP subproblem is the active set method due to Murray and Prieto (1995). The subproblems in both active set and interiorpoint methods may be solved by iterative (conjugate gradient like) methods, although it is crucial, especially for the latter, to use suitable preconditioners. Finally, as to which of the two QP alternatives we suggest is appropriate for SQP ....

W. Murray and F. J. Prieto. A sequential quadratic programming algorithm using an incomplete solution of the subproblem. SIAM Journal on Optimization, 5(3), 590--640, 1995.

....solution of the nonlinear state equation in every step, but as indicated above allow use of the structure of optimal control problems. In addition, SQP methods have proven to be very successful for the solution of other nonlinear programming problems. See e.g. 5] 9] 23] 24] 40] 47] [48], 50] 56] As outlined before, we use SQP based methods for the solution of (1.1) i.e. the all at once approach. However, the reduced problem (1.2) is important to us for two reasons. Firstly, the relation between the full problem (1.1) and the reduced problem (1.2) gives important insight ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590--640.

....reduce the gradient of f and the Hessian of the Lagrangian to the null space of J(x ) 28 3.2 SQP Algorithms We describe now SQP and reduced SQP algorithms for problem (3.1) SQP algorithms are very successful for the solution of constrained optimization problems. See e.g. 5] 59] 91] [108]. They are often quasi Newton type algorithms in the sense that they rely on a Newton iteration and approximate second order derivatives. The primary goal of these algorithms is to find a point that satisfies the first order necessary optimality conditions. So we proceed as in Chapter 2 and ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590--640.

....developed many iterative methods for solving (1.3) We refer to [14] for a comprehensive treatment of these methods. Among the iterative methods, the so called successive quadratic programming (SQP) method is considered one of the most important methods and has received much attention (see e.g. [1, 2, 3, 4, 6, 10, 15, 17, 18, 19, 24, 27, 28, 29, 30, 33]) In conventional SQP methods (see e.g. 17, 28, 29, 30] problem (1.1) is approximated by a sequence of quadratic programming problems min 1 2 p T B k p rf(x k ) T p s.t. g i (x k ) rg i (x k ) T p 0; i = 1; 2; m h j (x k ) rh j (x k ) T p = 0; j = 1; 2; r; 1:4) ....

MURRAY, W., and PRIETO, F., A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM Journal on Optimization, Vol. 5, pp. 590-640, 1995.

....of constraints. This technique is new, too. The choice of c results in a modification of the constraint values of those constraints with negative multipliers and makes the computed direction d uphill for those constraints. A similar scheme has been proposed independently by Murray and Prieto [27], however in the context of an incomplete solution of an inequality constrained QP. The algorithm computes new tentative penalty weights (named u and v below) in every step. These undergo a test of acceptability. This is done as described in [35] The method employed provides for an increase ....

W. Murray and J.P. Prieto, "A sequential quadratic programming algorithm using an incomplete solution of the subproblem", SIAM J. Optimization 5(1995), 590--640.

....trust region globalizations requires techniques different from those that can be used for line search globalizations. Other papers which investigate SQP methods for large scale problems, but without treatment of inexact linear systems solves and inexact derivative information include [1] 31] [36]. ANALYSIS OF INEXACT TRIP SQP ALGORITHMS 4 This paper is organized as follows. In Section 2, we state the first order necessary optimality conditions of problem (1.1) A review of the features of the exact TRIP SQP algorithms necessary for the inexact analysis is given in Section 3. The ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590--640.

....is enforced: c(x k k p k ) b (p k b x k x k ) 2.5) We use b i = V maxf1; c i (x 0 )g, where V is a speci ed constant, e.g. V = 10. This de nes a region in which the objective is expected to be de ned and bounded below. A similar condition is used in [70] Murray and Prieto [56] show that under certain conditions, convergence can be assured if the line search enforces (2.5) If the objective is bounded below in IR n then b may be any large positive vector. If k is essentially zero (because kp k k is very large) the objective is considered unbounded in the ....

....be needed for the rst QP, building up many degrees of freedom (superbasic variables) that are promptly eliminated by more thousands of iterations in the second QP. In general, it seems wasteful to expend much e ort on any QP before updating H k and the constraint linearization. Murray and Prieto [56] suggest one approach to terminating the QP solutions early, requiring that at least one QP stationary point be reached. The associated theory implies that any subsequent point b x k generated by a QP solver is suitable provided kbx k x k k is nonzero. In SNOPT we have implemented a method within ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590-640.

....feature of SQP methods, these examples illustrate that some caution is required. We anticipate that efficiency would be improved by allowing the QP subproblem to terminate early if the reduced Hessian dimension has increased significantly. Other criteria for early termination are discussed in [37]. A selection of problems with variable dimensions. The next selection was used to choose problems whose dimension can be one of several values. We chose n as close to 1000 as possible. Problems from the other 3 categories were deleted. Objective function type : Constraints type : Q O ....

W. Murray and F. J. Prieto, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, SIAM J. Optim., 5 (1995), pp. 590--640.

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W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using an incomplete solution of the subproblem, Tech Report, Department of Operations Research, Stanford University, (1992).

No context found.

W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using and incomplete solution of the subproblem, Tech Report, Department of Operations Research, Stanford University, (1992).

No context found.

W. Murray and F. J. Prieto ( to appear), `A sequential quadratic programming algorithm using an incomplete solution of the subproblem', SIAM Journal on Optimization. S. G. Nash and A. Sofer (1995), Linear and Nonlinear Programming, McGraw-Hill, New York.

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W. MURRAY AND F. J. PRIETO, A sequential quadratic programming algorithm using and incomplete solution of the subproblem, Tech Report, Department of Operations Research, Stanford University, (1992).

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