Characterization and recognition of d.c. functions

Ginchev, Ivan; Gintcheva, Denitza

doi:10.1007/s10898-012-9964-6

Cited by 7 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In particular, DC(R n ) contains the space C 1,1 of functions whose gradient is locally Lipschitz. Properties which help to recognize a DC function can be found, for instance in [18,29]. DC(R n ) is closed under the operations usually considered in optimization.…”

Section: Preliminariesmentioning

confidence: 99%

Global convergence of a proximal linearized algorithm for difference of convex functions

2015

View full text Add to dashboard Cite

ADInternational audienceA proximal linearized algorithm for minimizing difference of two convex functions is proposed. If the sequence generated by the algorithm is bounded it is proved that every cluster point is a critical point of the function under consideration, even if the auxiliary minimizations are performed inexactly at each iteration. Linear convergence of the sequence is established under suitable additional assumptions

show abstract

Section: Preliminariesmentioning

confidence: 99%

Global convergence of a proximal linearized algorithm for difference of convex functions

2015

View full text Add to dashboard Cite

show abstract

“…In some cases, it is assumed that the calculation of a single objective function value may take from a few minutes to several hours of continuous computer operation. Developing an effective global optimization method requires identifying certain properties of the objective function (and constraints), for example, determining a good estimate of the Lipschitz constant [1][2][3][4] or representing a function as a difference between two convex functions [5][6][7]. Such auxiliary problems do not always have a unique solution and are not often easily solvable.…”

Section: Introductionmentioning

confidence: 99%

Application of the Parabola Method in Nonconvex Optimization

Kolosnitsyn,

Khamisov,

Semenkin

et al. 2024

Algorithms

View full text Add to dashboard Cite

We consider the Golden Section and Parabola Methods for solving univariate optimization problems. For multivariate problems, we use these methods as line search procedures in combination with well-known zero-order methods such as the coordinate descent method, the Hooke and Jeeves method, and the Rosenbrock method. A comprehensive numerical comparison of the obtained versions of zero-order methods is given in the present work. The set of test problems includes nonconvex functions with a large number of local and global optimum points. Zero-order methods combined with the Parabola method demonstrate high performance and quite frequently find the global optimum even for large problems (up to 100 variables).

show abstract

“…Вышла статья [20], где речь идет об условиях представимости функции в виде разности выпуклых в бесконечномерных пространствах.…”

Section: Introductionunclassified

Conditions for representation of a function of many arguments as the difference of convex functions

Proudnikov

2017

Preprint

View full text Add to dashboard Cite

Characterization and recognition of d.c. functions

Cited by 7 publications

References 14 publications

Global convergence of a proximal linearized algorithm for difference of convex functions

Global convergence of a proximal linearized algorithm for difference of convex functions

Application of the Parabola Method in Nonconvex Optimization

Conditions for representation of a function of many arguments as the difference of convex functions

Contact Info

Product

Resources

About