On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems

Ma, Cheng; Zhang, Liansheng

doi:10.1016/j.amc.2015.09.020

Cited by 9 publications

(7 citation statements)

References 41 publications

(63 reference statements)

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“…The penalty function method is adopted to solve the optimization problem mentioned above, the basic idea of which is to convert the constraint into a penalty function according to the characteristics of the constraint and add it to the objective function, transforming the constrained optimization problem into an unconstrained one. [18][19][20] The penalty function method can be divided into external and internal penalty function methods; the one adopted in this study is the internal penalty function method. Figure 4 shows the flowchart to solve the optimization problem (equation ( 17)) using the internal penalty function method & min f ðxÞ s:t:…”

Section: Solving Methods For the Optimization Problemmentioning

confidence: 99%

Design and analysis of the mandrel structure for a composite S-shaped inlet

Hao

Jiang

2021

Proceedings of the Institution of Mechanical Engineers, Part G:

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Automated fiber placement (AFP) combining with the autoclave curing process is the main manufacturing method for large-scale rotary composite parts. During the forming process, the mandrel plays an important role that affects the forming quality of the part directly. In this study, design and analysis of the mandrel structure for a composite S-shaped inlet are carried out. The preforming process of the rotary composite part using the AFP technique is introduced first. Then, design principles of the shaft are presented and applied to the shaft design for the mandrel of the S-shaped inlet, which then is transformed into an optimization problem. The internal penalty function method is adopted to solve this optimization problem in order to obtain the optimal axis position and axle diameter. Moreover, detailed structure design of the mandrel is proposed which takes the demolding into consideration, and the wall thickness is designed considering the total weight and the stiffness. The static analysis and modal analysis are also carried out by the finite element method to verify the feasibility of the proposed mandrel structure.

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Section: Solving Methods For the Optimization Problemmentioning

confidence: 99%

Design and analysis of the mandrel structure for a composite S-shaped inlet

Hao

Jiang

2021

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…extended or parametric penalty function) was introduced by Huyer and Neumaier [22] in 2003. This penalty function was generalized and, later on, applied to various optimization problems in [1,35,24,30,26,23,25,31,39,13]. In [12], it was shown that Huyer and Neumaier's extended penalty function is exact if and only if the standard nonsmooth penalty function is exact, and some relations between the least exact penalty parameters of these functions were obtained.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness

Долгополик

2018

J Optim Theory Appl

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In the second part of our study we introduce the concept of global extended exactness of penalty and augmented Lagrangian functions, and derive the localization principle in the extended form. The main idea behind the extended exactness consists in an extension of the original constrained optimization problem by adding some extra variables, and then construction of a penalty/augmented Lagrangian function for the extended problem. This approach allows one to design extended penalty/augmented Lagrangian functions having some useful properties (such as smoothness), which their counterparts for the original problem might not possess. In turn, the global exactness of such extended merit functions can be easily proved with the use of the localization principle presented in this paper, which reduces the study of global exactness to a local analysis of a merit function based on sufficient optimality conditions and constraint qualifications. We utilize the localization principle in order to obtain simple necessary and sufficient conditions for the global exactness of the extended penalty function introduced by Huyer and Neumaier, and in order to construct a globally exact continuously differentiable augmented Lagrangian function for nonlinear semidefinite programming problems.

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“…Then, a penalty function is used to transform the NLP problem into an unconstrained one. In [11], a new exact and smooth penalty function for the MINLP problem is presented by augmenting only one variable whatever the number of constraints.…”

Section: Introductionmentioning

confidence: 99%

Continuous Relaxation of MINLP Problems by Penalty Functions: A Practical Comparison

Costa

Rocha

Fernandes

2017

Computational Science and Its Applications – ICCSA 2017

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A practical comparison of penalty functions for globally solving mixed-integer nonlinear programming (MINLP) problems is presented. The penalty approach relies on the continuous relaxation of the MINLP problem by adding a specific penalty term to the objective function. A new penalty algorithm that addresses simultaneously the reduction of the error tolerances for optimality and feasibility, as well as the reduction of the penalty parameter, is designed. Several penalty terms are tested and different penalty parameter update schemes are analyzed. The continuous nonlinear optimization problem is solved by the deterministic DIRECT optimizer. The numerical experiments show that the quality of the produced solutions are satisfactory and that the selected penalties have different performances in terms of efficiency and robustness.

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On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems

Cited by 9 publications

References 41 publications

Design and analysis of the mandrel structure for a composite S-shaped inlet

Design and analysis of the mandrel structure for a composite S-shaped inlet

A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness

Continuous Relaxation of MINLP Problems by Penalty Functions: A Practical Comparison

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