A New Smooth Method for the l1 Exact Penalty Function for Inequality Constrained Optimization

Wang, Zhijie; Liu, Sanming

doi:10.1109/cso.2010.157

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…Since inequalities (36)(37)(38)(39)(40) are satisfied for any x ∈ S, they are also satisfied for any x ∈ D. Thus, by the feasibility of x in problem (P) and (9), inequalities (38-40) yield, respectively,…”

Section: Are Convex Atx On S Thenx Is Also a Lu-optimal Solution Of mentioning

confidence: 98%

“…It is due to the fact that the penalty term in this function involves the l 1 norm of the violated constraints. The exact l 1 penalty function method has been researched widely for solving constrained optimization problems (see, for instance, Antczak [21,22], Bazaraa et al [23], Bertsekas [24], Bertsekas and Koksal [25], Bonnans et al [26], Charalambous [27], Di Pillo and Grippo [28], Fletcher [29,30], Janesch and Santos [31], Mangasarian [32], Mongeau and Sartenaer [33], Nocedal and Wright [34], Peressini et al [35], Wang and Liu [36], and others).…”

Section: Introductionmentioning

confidence: 99%

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Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Antczak

2017

J Optim Theory Appl

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In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.Keywords Interval-valued optimization problem · Exact absolute value penalty function method · Penalized optimization problem with the interval-valued exact absolute value penalty function · Exactness of the exact absolute value penalty function method · LU-convex function Mathematics Subject Classification 49M30 · 90C25 · 90C30Communicated by

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Section: Are Convex Atx On S Thenx Is Also a Lu-optimal Solution Of mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Antczak

2017

J Optim Theory Appl

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“…The AlexNet [7] convolutional neural network (CNN) architecture was the champion of the ImageNet challenge competition in 2012. Since then, many excellent neural network algorithms have emerged, such as the VGG [8], Inception [9], and ResNet [10], which constantly set records and set off waves of artificial intelligence.…”

Section: Introductionmentioning

confidence: 99%

Implementation of a Modified Faster R-CNN for Target Detection Technology of Coastal Defense Radar

Chen

Jin

et al. 2021

Remote Sensing

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The traditional method of constant false-alarm rate detection is based on the assumption of an echo statistical model. The target recognition accuracy rate and the high false-alarm rate under the background of sea clutter and other interferences are very low. Therefore, computer vision technology is widely discussed to improve the detection performance. However, the majority of studies have focused on the synthetic aperture radar because of its high resolution. For the defense radar, the detection performance is not satisfactory because of its low resolution. To this end, we herein propose a novel target detection method for the coastal defense radar based on faster region-based convolutional neural network (Faster R-CNN). The main processing steps are as follows: (1) the Faster R-CNN is selected as the sea-surface target detector because of its high target detection accuracy; (2) a modified Faster R-CNN based on the characteristics of sparsity and small target size in the data set is employed; and (3) soft non-maximum suppression is exploited to eliminate the possible overlapped detection boxes. Furthermore, detailed comparative experiments based on a real data set of coastal defense radar are performed. The mean average precision of the proposed method is improved by 10.86% compared with that of the original Faster R-CNN.

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“…The most popular nondifferentiable exact penalty function is the absolute value penalty function, also called the exact l 1 penalty function. The nondifferentiable exact absolute penalty function method has been investigated in Bazaraa et al (1991), Bertsekas and Koksal-Ozdaglar (2000), Charalambous (1978), Di Pillo and Grippo (1989), Dolecki and Rolewicz (1979), Fletcher (1973), Han and Mangasarian (1979), Luenberger (1970), Mangasarian (1985), Peressini et al (1988), Wang and Liu (2010), Yang and Ralph (2005), and others.…”

Section: Introductionmentioning

confidence: 99%

Exactness of the absolute value penalty function method for nonsmooth ‐invex optimization problems

Antczak

2017

Int Trans Operational Res

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In this paper, the classical exact absolute value penalty function method is used for solving a new class of nonconvex nonsmooth optimization problems. Nonconvex nondifferentiable optimization problems with both inequality and equality constraints are considered here, in which not all functions constituting them have the fundamental property of convex functions and most classes of generalized convex functions-namely, a stationary point of such a function is its global minimum. It is proved for such nonconvex optimization problems that there exists a finite threshold of penalty parameters equal to the largest absolute value of a Lagrange multiplier such that, for every penalty parameter exceeding this lower bound, there is the equivalence between an optimal solution in the original constrained minimization problem with ( , ρ)-invex functions and a minimizer in its associated penalized optimization problem with the exact l 1 penalty function. Further, under nondifferentiable ( , ρ)-invexity assumptions, a characterization of a saddle point of the Lagrange function, defined for the considered constrained optimization problem in terms of minimizers of its associated exact penalized optimization problem with the exact l 1 penalty function, is presented.

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A New Smooth Method for the l1 Exact Penalty Function for Inequality Constrained Optimization

Cited by 4 publications

References 14 publications

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Implementation of a Modified Faster R-CNN for Target Detection Technology of Coastal Defense Radar

Exactness of the absolute value penalty function method for nonsmooth ‐invex optimization problems

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