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6th International Conference on Control and Optimization with Industrial Applications (COIA) -- JUL 11-13, 2018 -- Baku, AZERBAIJAN, WOS: 000463894700061, …, Minist Transport Commun & High Technologies Republ Azerbaijan, Baku State Univ, Inst Appl Math

6th International Conference on Control and Optimization with Industrial Applications (COIA) -- JUL 11-13, 2018 -- Baku, AZERBAIJAN, WOS: 000463893800039, …, Minist Transport Commun & High Technologies Republ Azerbaijan, Baku State Univ, Inst Appl Math

WOS: 000304274600001, …

This paper deals with the weak subdifferentials. The properties of the weak subdifferentials are examined. It is showed that the weak subdifferential of a function having a global minimum is not empty.Key Words: Subdifferential, Weak subgradient, Weak subdifferential.&nbsp

24th Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector, MEC EurOPT 2010 -- 23 June 2010 through 26 June 2010 -- Izmir -- 106702, In this paper, the generalized radial epiderivative for set-valued maps is introduced and its relationship to the radial epiderivative is investigated. Existence conditions for generalized radial epiderivatives are established and unified necessary and sufficient optimality condition in nonconvex setvalued optimization is derived in terms of the generalized radial epiderivative

WOS: 000477052300001, The paper presents an analysis, characterizations and comparison of six commonly used scalarization methods in multiobjective optimization. The properties of these methods are investigated with respect to the basic characteristics such as ordering cone, convexity and boundedness, the ability of generating proper efficient solutions, the ability to consider reference points which is a choice of decision maker as a solution and weighting preferences of decision maker, the number of additional constraints and decision variables. The paper also presents new characteristics for these methods and relations between them. The main characteristics of these scalarization methods are illustrated on the same example., Anadolu University Scientific Research Projects Commission [1304F062], This study was supported by Anadolu University Scientific Research Projects Commission under the Grant No. 1304F062.

WOS: 000455496800005, Coaches of sports clubs aim to form the team that optimally determines the roles of positions before the match. These types of decisions are referred to as the team formation problem, and they are critical for the sports industry in the financial sense. Finding the optimal solution to the team formation problem is more difficult without the use of systematical approaches, as the number of players and their past performance records have increased substantially in recent years. In this paper, we discuss previous studies on the team formation problems of sports clubs and outline the deficiencies of their results in real-life decision processes. Then, we propose two new formulations that address coaches' preferences in the decision-making process. A real-life application of the proposed models is displayed for a volleyball team that participates in the first division of the Turkish Volleyball League.

WOS: 000393534400018, This paper investigates some properties of approximate efficiency in variable ordering structures where the variable ordering structure is given by a special set valued map. We characterize epsilon-minimal and epsilon- nondominated elements as approximate solutions of a multiobjective optimization problem with a variable ordering structure and give necessary and sufficient conditions for these solutions, via scalarization

WOS: 000361624700018, In this paper, a piecewise linear classifier based on polyhedral conic separation is developed. This classifier builds nonlinear boundaries between classes using polyhedral conic functions. Since the number of polyhedral conic functions separating classes is not known a priori, an incremental approach is proposed to build separating functions. These functions are found by minimizing an error function which is nonsmooth and nonconvex. A special procedure is proposed to generate starting points to minimize the error function and this procedure is based on the incremental approach. The discrete gradient method, which is a derivative-free method for nonsmooth optimization, is applied to minimize the error function starting from those points. The proposed classifier is applied to solve classification problems on 12 publicly available data sets and compared with some mainstream and piecewise linear classifiers., Australian Research Council [DP140103213], The authors would like to thank three anonymous referees for their criticism and comments which allowed to improve the quality of the paper. The research by Dr. A.M. Bagirov was supported under Australian Research Council's Discovery Projects funding scheme (Project No. DP140103213).

Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.

WOS: 000345083300008, In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions., Deutsche Forschungsgesellschaft (DFG) [EI 821/2-1], The authors are grateful to Truong Xuan Duc Ha from the Institute of Mathematics in Hanoi for valuable comments on the elements of the augmented dual cone of a Bishop-Phelps cone. The research of this work was supported by the grant EI 821/2-1 from the Deutsche Forschungsgesellschaft (DFG) and was mainly prosecuted during a stay of the second author at the Institute of Mathematics, Technische Universitat Ilmenau.

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