Subdifferentials of a perturbed minimal time function in normed spaces

Zhang, Yongle; He, Yong; Jiang, Yi

doi:10.1007/s11590-013-0689-3

Cited by 6 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, we generalize and validate the results obtained recently by Zhang, He, and Jiang in [14].…”

Section: Introductionsupporting

confidence: 87%

“…Note that we only assume that f satisfies a center-Lipschitz condition on its domain instead of the whole space X as in [14]. This is important because the indicator function δ Ω obviously satisfies a center-Lipschitz condition on its domain Ω with constant ℓ = 0, but it does not satisfies a center-Lipschitz condition on X.…”

Section: Proposition 22mentioning

confidence: 99%

“…In a recent paper published in Optimization Letters, Zhang, He, and Jiang [14] introduced and studied the so-called perturbed minimal time function…”

Section: Introductionmentioning

confidence: 99%

“…Using Corollary 2.4 and the fact that the norm function is coercive with constant m = 1, it is easy to obtain the related results from [8,13], as well as the results from [14,Corollary 3.1] and [14,Corollary 3.2] without assuming the convexity of the set S therein. Note that it is not possible to apply [14,Theorem 3.1] to derive these results since the function f (x) := J(x) + δ(x; Ω) never satisfies a center-Lipschitz condition atx ∈ S 0 if Ω is a proper subset of X.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Subdifferential formulas for a class of non-convex infimal convolutions

Nam

2014

Optimization

View full text Add to dashboard Cite

show abstract

“…In particular, we generalize and validate the results obtained recently by Zhang, He, and Jiang in [14].…”

Section: Introductionsupporting

confidence: 87%

Section: Proposition 22mentioning

confidence: 99%

“…In a recent paper published in Optimization Letters, Zhang, He, and Jiang [14] introduced and studied the so-called perturbed minimal time function…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Subdifferential formulas for a class of non-convex infimal convolutions

Nam

2014

Optimization

View full text Add to dashboard Cite

show abstract

“…The readers are referred to [4,5,8,9,12,14,15,17,19,21,22,25,26] and the references therein for the study of the minimal time function as well as its specification to the case of the distance function.…”

Section: Introductionmentioning

confidence: 99%

Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

Nam

Cuong

2014

Set-Valued Var. Anal

View full text Add to dashboard Cite

Abstract. This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas obtained unify several known results and allow us to characterize the differentiability of the infimal convolution which plays an important role in variational analysis and optimization.

show abstract

A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality

Grad

Wilfer

2019

J Glob Optim

View full text Add to dashboard Cite

We investigate via a conjugate duality approach general nonlinear minmax location problems formulated by means of an extended perturbed minimal time function, necessary and sufficient optimality conditions being delivered together with characterizations of the optimal solutions in some particular instances. A parallel splitting proximal point method is employed in order to numerically solve such problems and their duals. We present the computational results obtained in matlab on concrete examples, successfully comparing these, where possible, with earlier similar methods from the literature. Moreover, the dual employment of the proximal method turns out to deliver the optimal solution to the considered primal problem faster than the direct usage on the latter. Since our technique successfully solves location optimization problems with large data sets in high dimensions, we envision its future usage on big data problems arising in machine learning.Keywords Gauge (Minkowski) function · Minimal time function · Minmax multifacility location problem · Sylvester problem · Apollonius problem · Proximal point algorithm · Epigraphical projection · Projection operator · Machine learning 1 PreliminariesIn this paper we investigate nonlinear minmax location problems that are generalizations of the classical Sylvester problem in location theory-not to be confused with Sylvester's line

show abstract

Subdifferentials of a perturbed minimal time function in normed spaces

Cited by 6 publications

References 16 publications

Subdifferential formulas for a class of non-convex infimal convolutions

Subdifferential formulas for a class of non-convex infimal convolutions

Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality

Contact Info

Product

Resources

About