Aggregate codifferential method for nonsmooth DC optimization

Tor, Ali Hakan
Bagirov, Adil
Karasözen, Bülent
A new algorithm is developed based on the concept of codifferential for minimizing the difference of convex nonsmooth functions. Since the computation of the whole codifferential is not always possible, we use a fixed number of elements from the codifferential to compute the search directions. The convergence of the proposed algorithm is proved. The efficiency of the algorithm is demonstrated by comparing it with the subgradient, the truncated codifferential and the proximal bundle methods using nonsmooth optimization test problems.


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A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as th...
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In this thesis, various numerical methods are developed to solve nonsmooth and in particular, nonconvex optimization problems. More specifically, three numerical algorithms are developed for solving nonsmooth convex optimization problems and one algorithm is proposed to solve nonsmooth nonconvex optimization problems. In general, main differences between algorithms of smooth optimization are in the calculation of search directions, line searches for finding step-sizes and stopping criteria. However, in nonsmoo...
Efe, Giray; Cenk, Murat; Department of Cryptography (2022-3-07)
Polynomial multiplication on the quotient ring Z[x]/<x^n+-1> is one of the most fundamental, general-purpose operations frequently used in cryptographic algorithms. Therefore, a possible improvement over a multiplication algorithm directly affects the performance of algorithms used in a cryptographic application. Well-known multiplication algorithms such as Schoolbook, Karatsuba, and Toom-Cook are dominant choices against NTT in small and ordinary input sizes. On the other hand, how these approaches are imp...
Characterisation and enumeration of a class of semi bent quadratic Boolean functions
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In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Citation Formats
A. H. Tor, A. Bagirov, and B. Karasözen, “Aggregate codifferential method for nonsmooth DC optimization,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 851–867, 2014, Accessed: 00, 2020. [Online]. Available: