Incremental DC optimization algorithm for large-scale clusterwise linear regression
- Authors: Bagirov, Adil , Taheri, Sona , Cimen, Emre
- Date: 2021
- Type: Text , Journal article
- Relation: Journal of Computational and Applied Mathematics Vol. 389, no. (2021), p. 1-17
- Relation: https://purl.org/au-research/grants/arc/DP190100580
- Full Text: false
- Reviewed:
- Description: The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental approach is designed to solve the CLR problem. We apply the Quasi-Newton method to solve the subproblems. The proposed algorithm is evaluated using several synthetic and real-world data sets for regression and compared with other algorithms for CLR. Results demonstrate that the DCA based algorithm is efficient for solving CLR problems with the large number of data points and in particular, outperforms other algorithms when the number of input variables is small. © 2020 Elsevier B.V.
Conditions for global optimality of quadratic minimization problems with LMI constraints
- Authors: Jeyakumar, Vaithilingam , Wu, Zhiyou
- Date: 2007
- Type: Text , Journal article
- Relation: Asia-Pacific Journal of Operational Research Vol. 24, no. 2 (2007), p. 149-160
- Full Text: false
- Reviewed:
- Description: In this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) cnstraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints. © World Scientific Publishing Co. & Operational Research Society of Singapore.
- Description: C1
Increasing quasiconcave co-radiant functions with applications in mathematical economics
- Authors: Martinez-Legaz, Juan , Rubinov, Alex , Schaible, Siegfried
- Date: 2005
- Type: Text , Journal article
- Relation: Mathematical Methods of Operations Research Vol. 61, no. 2 (2005), p. 261-280
- Full Text: false
- Reviewed:
- Description: We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In particular we identify a small "natural" infimal generator of the set of all coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of production functions and utility functions are discussed. © Springer-Verlag 2005.
- Description: C1
- Description: 2003001423
Stability of semi-infinite inequality systems involving min-type functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 81-112
- Full Text: false
- Reviewed:
- Description: We study the stability of semi-infinite inequality systems that arise in monotonic analysis. These systems are defined by certain classes of abstract linear functions. We consider the cone R
- Description: C1
- Description: 2003001420
Stability of the lower level sets of ICAR functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 113-127
- Full Text: false
- Reviewed:
- Description: In this paper, we study the stability of the lower level set {x E R++n | f (x) ≤ 0} of a finite valued increasing convex-along-rays (ICAR) function f defined on R++n. In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of R ++n. The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. Copyright © Taylor & Francis, Inc.
- Description: C1
- Description: 2003001419
The zero duality gap property and lower semicontinuity of the perturbation function
- Authors: Rubinov, Alex , Huang, X. X. , Yang, Xiao
- Date: 2002
- Type: Text , Journal article
- Relation: Mathematics of Operations Research Vol. 27, no. 4 (2002), p. 775-791
- Full Text: false
- Reviewed:
- Description: We examine the validity of the zero duality gap properties for two important dual schemes: a generalized augmented Lagrangian dual scheme and a nonlinear Lagrange-type dual scheme. The necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions.
- Description: 2003000117