Sequential Quadratic Programming Methods

Gill, Philip E.; Wong, Elizabeth

doi:10.1007/978-1-4614-1927-3_6

Cited by 143 publications

(81 citation statements)

References 135 publications

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“…So, if the matrix in the left-hand side is nonsingular, then the linear system (20), (21) has the unique solution (ξ j , η j ). Since equations (20), (21) are equivalent to the Lagrange system of the sSQP subproblem, (ξ j , η j ) is also the unique stationary point of this subproblem.…”

Section: The Algorithm and Its Convergence Propertiesmentioning

confidence: 99%

“…Here, we only mention that sSQP has local superlinear convergence under the second-order sufficient optimality condition only, without any constraints qualification assumptions [12] (for equality-constrained problems, even the weaker noncriticality condition is enough [29]). This should be contrasted with the usual SQP method [6,20] (see also [31,Chapter 4]), which in addition requires relatively strong regularity condition on the constraints (while sSQP needs nothing at all). We note that very few globalizations of the local sSQP scheme have been proposed so far, all very recently.…”

Section: Introductionmentioning

confidence: 99%

“…Sufficient positive definiteness of the matrix (i.e., the fulfillment of (19)) can be achieved by modifying it in the process of its Cholesky factorization [36,Section 3.4], if this is the approach for computing the solution ξ j of the linear system (21). Then η j is given by the explicit formula (20).…”

Section: The Algorithm and Its Convergence Propertiesmentioning

confidence: 99%

See 2 more Smart Citations

Combining stabilized SQP with the augmented Lagrangian algorithm

2015

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For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type for approximately solving subproblems of the augmented Lagrangian method. The motivation is to take advantage of the well-known robust behavior of the augmented Lagrangian algorithm, including on problems with degenerate constraints, and at the same time try to reduce the overall algorithm locally to sSQP (which gives fast local convergence rate under weak assumptions). Specifically, the algorithm first verifies whether the primal-dual sSQP step (with unit stepsize) makes good progress towards decreasing the violation of optimality conditions for the original problem, and if so, makes this step. Otherwise, the primal part of the sSQP direction is used for linesearch that decreases the augmented Lagrangian, keeping the multiplier estimate fixed for the time being. The overall algorithm has reasonable global convergence guarantees, and inherits strong local convergence rate properties of sSQP under the same weak assumptions. Numerical results on degenerate problems and comparisons with some alternatives are reported.

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Section: The Algorithm and Its Convergence Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combining stabilized SQP with the augmented Lagrangian algorithm

2015

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“…(8)) is a nonlinearprogramming model. The nonlinear programming characteristic causes the model to be adequately hard to solve by exact methods (Gen, 1997), But since SQP is a powerful and effective class of exact algorithms for a wide range of nonlinear optimization problems (Gill et al 2010). We will solve mentioned model aided to SQP exact algorithm.…”

Section: Mathematical Modelmentioning

confidence: 99%

Optimization of rewards in single machine scheduling in the rewards-driven systems

Gharaei¹,

Naderi²,

Mohammadi

2015

10.5267/j.msl

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The single machine scheduling problem aims at obtaining the best sequence for a set of jobs in a manufacturing system with a single machine. In this paper, we optimize rewards in single machine scheduling in rewards-driven systems such that total reward is maximized while the constraints contains of limitation in total rewards for earliness and learning, independent of earliness and learning and etc. are satisfied. In mentioned systems as for earliness and learning the bonus is awarded to operators, we consider only rewards in mentioned systems and it will not be penalized under any circumstances. Our objective is to optimize total rewards in mentioned system by taking the rewards in the form of quadratic for both learning and earliness. The recently-developed sequential quadratic programming (SQP), is used by solve the problem. Results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error. Finally, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the "amount of earliness for jobs (Ei parameter)".Growing Science Ltd. All rights reserved. 5

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“…Further details about the SQP class of algorithms can be found on the review papers of Boggs and Tolle [19] and Gill and Wong [20]. This technique was found to be adequate because of the non-linearity of both the fitness function and the constraints considered.…”

Section: Optimization Techniquementioning

confidence: 99%

Analysis and optimization of agro waste composite beam structures

Loja

Silva²,

Barbosa³

2013

uujms

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The present work, is focused on the study of beam type structures made of agro waste composite materials, namely of sawdust and palm kernel shell, and comprises two parts. A first one where the static and dynamic behavior characterization of the structure is carried out using a first order shear deformation theory approach, considering the influence of different fiber constituent's percentages. In the second part, a few structural optimization case studies are considered concerning different objective functions and constraints, using sequential quadratic programming technique. Both, analysis and optimization studies were developed on a symbolic computation platform. According to the results obtained in the case studies carried out, it can be concluded that they respect the trends that would be expected, taking into account the nature of the parameters studied: the length to thickness ratio, the boundary conditions and the percentages of the reinforcement agents' mixtures. A final aspect that is worth mentioning is related to the advantages of using such type of platform in research work, which enables for an integrated development and simulation environment, where the libraries access and the functionalities available, enable a more expedite and perceptive way of achieving results.

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Sequential Quadratic Programming Methods

Cited by 143 publications

References 135 publications

Combining stabilized SQP with the augmented Lagrangian algorithm

Combining stabilized SQP with the augmented Lagrangian algorithm

Optimization of rewards in single machine scheduling in the rewards-driven systems

Analysis and optimization of agro waste composite beam structures

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