A new smoothing approach to exact penalty functions for inequality constrained optimization problems

Şahiner, Ahmet; Kapusuz, Gülden; Yılmaz, Nurullah

doi:10.3934/naco.2016006

Cited by 13 publications

(8 citation statements)

References 17 publications

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“…From (25) and (26), we obtain S α R f −→ f pointwise, as α −→ +∞. Now, let us analyze the error estimates.…”

Section: Smoothing Approximations For One-dimensional Case Let Us Consider the Partitionmentioning

confidence: 99%

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Smoothing approximations for piecewise smooth functions: A probabilistic approach

Amhraoui¹,

Masrour²

2022

NACO

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<p style='text-indent:20px;'>In this article, we present a new approach to construct smoothing approximations for piecewise smooth functions. This approach proposes to formulate any piecewise smooth function as the expectation of a random variable. Based on this formulation, we show that smoothing all elements of a defined space of piecewise smooth functions is equivalent to smooth a single probability distribution. Furthermore, we propose to use the Boltzmann distribution as a smoothing approximation for this probability distribution. Moreover, we present the theoretical results, error estimates, and some numerical examples for this new smoothing method in both one-dimensional and multiple-dimensional cases.</p>

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“…From (25) and (26), we obtain S α R f −→ f pointwise, as α −→ +∞. Now, let us analyze the error estimates.…”

Section: Smoothing Approximations For One-dimensional Case Let Us Consider the Partitionmentioning

confidence: 99%

“…In fact, most of the exact penalty functions are not smooth. Therefore, many papers studied the smoothing approximations for these exact penalty functions [11,14,17,18,25]. As a result, smoothing techniques of P-S functions play a fundamental role in optimization and penalty methods.…”

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confidence: 99%

Smoothing approximations for piecewise smooth functions: A probabilistic approach

Amhraoui¹,

Masrour²

2022

NACO

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“…In order to improve the smoothing approaches, different types of valuable techniques and algorithms are developed [11][12][13][14]. In recent years, the smoothing approaches have been used for many non-smooth problems such as minmax [15,16], exact penalty [17][18][19][20] and etc. [21].…”

Section: Introductionmentioning

confidence: 99%

A new auxiliary function approach for inequality constrained global optimization problems

Yılmaz

Şahiner

2019

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this study, we deal with the nonlinear constrained global optimization problems. First, we introduce a new smooth exact penalty function for constrained optimization problems. We combine the exact penalty function with the auxiliary function in regard to constrained global optimization. We present a new auxiliary function approach and the adapted algorithm for solving non-linear inequality constrained global optimization problems. Finally, we illustrate the efficiency of the algorithm on some numerical examples.

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“…. , m. If q pi (t) = max{0, t} pi , then the function θ can be considered as penalty term in constrained optimization [34]. If q pi (t) = |t| pi , the function θ can be used as a regularization term in solving inverse problems [6].…”

mentioning

confidence: 99%

“…, 6 are presented in the Table 3. We consider the penalty approach in [34] to solve the problem given in (13) Table 3. The values of a j , b j and p j in Example 2…”

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confidence: 99%

On a new smoothing technique for non-smooth, non-convex optimization

Yılmaz¹,

Şahiner²

2020

NACO

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In many global optimization techniques, the local search methods are used for different issues such as to obtain a new initial point and to find the local solution rapidly. Most of these local search methods base on the smoothness of the problem. In this study, we propose a new smoothing approach in order to smooth out non-smooth and non-Lipschitz functions playing a very important role in global optimization problems. We illustrate our smoothing approach on well-known test problems in the literature. The numerical results show the efficiency of our method.

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A new smoothing approach to exact penalty functions for inequality constrained optimization problems

Cited by 13 publications

References 17 publications

Smoothing approximations for piecewise smooth functions: A probabilistic approach

Smoothing approximations for piecewise smooth functions: A probabilistic approach

A new auxiliary function approach for inequality constrained global optimization problems

On a new smoothing technique for non-smooth, non-convex optimization

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