Generalized exponential penalty function for nonlinear programming

Qin, Jiangning; Nguyen, Duc T.

doi:10.1016/0045-7949(94)90021-3

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…Discrete constraint aggregation techniques can be used to alleviate the computational cost of constraint gradient evaluation by aggregating local stress constraints into a single equivalent constraint [1,23,17]. The most common discrete constraint aggregation technique is the discrete Kreisselmeier-Steinhauser (KS) function, originally developed for control systems design [14], and subsequently adapted to a wide range of structural and multidisciplinary design optimization problems [24,29,1,23,16,8,21,12,17,18,13]. While discrete constraint aggregation reduces the computational cost of gradient evaluation, these methods also increase the nonlinearity in the design problem.…”

Section: Introductionmentioning

confidence: 99%

A Full-Space Method with Matrix Aggregates for Stress-Constrained Structural Optimization

Kennedy

2015

16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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Stress-constrained structural optimization is challenging due to the nature of the local stress constraints that must be imposed point-wise everywhere within the structural domain. These constraints lead to optimization problems for which classical reduced-space methods scale poorly with increasing number of local stress constraints. To address this issue, a full-space barrier method is developed which is designed for problems with large numbers of constraints. Within this method, local stress constraints are formulated as matrix inequalities using convex optimization methods. Matrix aggregates are introduced which aggregate local stress constraints formulated as linear matrix inequalities. The advantage of the linear matrix inequality formulation is that the resulting stress constraints are convex in both the design and state variables, where non-convexity enters only through the governing equations. The proposed method is demonstrated on a plane stress problem.

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Section: Introductionmentioning

confidence: 99%

A Full-Space Method with Matrix Aggregates for Stress-Constrained Structural Optimization

Kennedy

2015

16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…The smoothed version of the ∞ penalty function used in this paper was also used by [30,37,20,21]. Note that Liuzzi and Lucidi [20] and Liuzzi et al [21] explore properties of this function in the context of derivative-free programming and also handle linear constraints explicitly.…”

Section: This Impliesmentioning

confidence: 99%

“…The last smooth penalty function described in §4 approximates the ∞ function and has been used in [30,37,20,21]. Qin and Nguyen [30] first proposed using this smoothing in the context of nonlinear programming.…”

Section: Related Workmentioning

confidence: 99%

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Nonlinearly-constrained optimization using asynchronous parallel generating set search.

Griffin¹,

Kolda²

2007

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Many optimization problems in computational science and engineering (CS&E) are characterized by expensive objective and/or constraint function evaluations paired with a lack of derivative information. Direct search methods such as generating set search (GSS) are well understood and efficient for derivative-free optimization of unconstrained and linearly-constrained problems. This paper addresses the more difficult problem of general nonlinear programming where derivatives for objective or constraint functions are unavailable, which is the case for many CS&E applications. We focus on penalty methods that use GSS to solve the linearly-constrained problems, comparing different penalty functions. A classical choice for penalizing constraint violations is 2 2 , the squared 2 norm, which has advantages for derivative-based optimization methods. In our numerical tests, however, we show that exact penalty functions based on the 1, 2, and ∞ norms converge to good approximate solutions more quickly and thus are attractive alternatives. Unfortunately, exact penalty functions are discontinuous and consequently introduce theoretical problems that degrade the final solution accuracy, so we also consider smoothed variants. Smoothed-exact penalty functions are theoretically attractive because they retain the differentiability of the original problem. Numerically, they are a compromise between exact and 2 2 , i.e., they converge to a good solution somewhat quickly without sacrificing much solution accuracy. Moreover, the smoothing is parameterized and can potentially be adjusted to balance the two considerations. Since many CS&E optimization problems are characterized by expensive function evaluations, reducing the number of function evaluations is paramount, and the results of this paper show that exact and smoothed-exact penalty functions are well-suited to this task.3

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Parallel optimal control with multiple shooting, constraints aggregation and adjoint methods

Jeon

2005

JAMC

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Generalized exponential penalty function for nonlinear programming

Cited by 8 publications

References 12 publications

A Full-Space Method with Matrix Aggregates for Stress-Constrained Structural Optimization

A Full-Space Method with Matrix Aggregates for Stress-Constrained Structural Optimization

Nonlinearly-constrained optimization using asynchronous parallel generating set search.

Parallel optimal control with multiple shooting, constraints aggregation and adjoint methods

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