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 11 publications

(8 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Smoothing approximations for piecewise smooth functions: A probabilistic approach

Amhraoui¹,

Masrour²

2022

NACO

View full text Add to dashboard Cite

<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>

show abstract

“…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.…”

mentioning

confidence: 99%

Smoothing approximations for piecewise smooth functions: A probabilistic approach

Amhraoui¹,

Masrour²

2022

NACO

View full text Add to dashboard Cite

show abstract

“…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)

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…. , 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…”

mentioning

confidence: 99%

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

Yılmaz¹,

Şahiner²

2020

NACO

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 11 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

Contact Info

Product

Resources

About