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Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Open Access Research Article

Convex separable optimization

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pp. 1–10Online FirstMay 2026DOI: 10.47974/JIOS-2227XML
Received:
01 Oct 2025
Published Online:
15 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-2227
Pages:
1–10

Abstract

The special case of  convex separable optimization is considered in this paper. Relations between an admissible solution and an optimal solution of the initial separable optimization problem (SP), approximate separable problem (ASP), and linear approximate separable problem (LASP) are considered. The problem of mesh (grid) point generation, which is important about accuracy of the approximation process for the separable problem, is also considered. Estimates of the accuracy of the particular piecewise linear approximation, which is used, are presented. 

Keywords

Subject Classifications

90C25

References

[1] J. R. Brown, “Bounded knapsack sharing”, Mathematical Programming, vol. 67, no. 3, pp. 343-382 (1994). 
[2] D. S. Hochbaum, and J. G. Shanthikumar, “Convex separable optimization is not too much harder than linear optimization”, Journal of the ACM, vol. 37, no. 4, pp. 843-862 (1990). 
[3] J. J. Moré, and S. A. Vavasis, “On the solution of concave knapsack problems”, Mathematical Programmming, vol. 49, no. 3, pp. 397-411 (1991). 
[4] P. M. Pardalos, and N. Kovoor, “An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds”, Mathematical Programming, vol. 46, no. 3, pp. 321-328 (1990). 
[5] P. M. Pardalos, Y. Ye, and C.-G. Han, “Algorithms for the solution of quadratic knapsack problems”, Linear Algebra and Its Applications, vol. 152, pp. 69-91 (1991). 
[6] A. G. Robinson, N. Jiang, and C. S. Lerme, “On the continuous quadratic knapsack problem”, Mathematical Programming, vol. 55, no. 1, pp. 99-108 (1992). 
[7] S. M. Stefanov, “Convex separable minimization subject to bounded variables”, Computational Optimization and Applications. An International Journal, vol. 18, no. 1, pp. 27-48 (2001). 
[8] S. M. Stefanov, “Minimization of a convex linear-fractional separable function subject to a convex inequality constraint or linear equality constraint and bounds on the variables” Applied Mathematics Research eXpress, vol. 2006, no. 4, Article ID 36581, 24 pages (2006). 
[9] S. M. Stefanov, “Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints”, Journal of Interdisciplinary Mathematics, vol. 12, no. 5, pp. 647-673 (2009). 
[10] S. M. Stefanov, “Solution of some convex separable resource allocation and production planning problems with bounds on the variables”, Journal of Interdisciplinary Mathematics, vol. 13, no. 5, pp. 541-569 (2010). 
[11] S. M. Stefanov, “Well-posedness and primal-dual analysis of some convex separable optimization problems”, Advances in Operations Research, vol. 2013, Article ID 279030, 10 pages (2013). 
[12] S. M. Stefanov, “On the application of iterative methods of nondifferentiable optimization to some problems of approximation theory,” Mathematical Problems in Engineering, vol. 2014, Article ID 165701, 10 pages (2014). 
[13] S. M. Stefanov, “On the solution of multidimensional convex separable continuous knapsack problem with bounded variables”, European Journal of Operational Research, vol. 247, no. 2, pp. 366-369 (2015). 
[14] S. M. Stefanov, “Strictly convex separable optimization with linear equality constraints and bounded variables”, Journal of Statistics and Management Systems, vol. 21, no. 2, pp. 261-272 (2018). 
[15] S. M. Stefanov, “On the solution of quadratic programming problem with a feasible region defined as a Minkowski sum of a compact set and finitely generated convex closed cone”, Journal of Information and Optimization Sciences, vol. 39, no. 6, pp. 1223-1230 (2018). 
[16] S. M. Stefanov, “Characterization of the optimal solution of the convex generalized nonlinear transportation problem”, Journal of Interdisciplinary Mathematics, vol. 22, no. 5, pp. 745-756 (2019). 
[17] S. M. Stefanov, “Characterization of the optimal solution of the convex separable continuous knapsack problem and related problems”, Journal of Information and Optimization Sciences, vol. 42, no. 1, pp. 1-16 (2021). 
[18] S. M. Stefanov, “On the numerical solution of separable stochastic inventory control problems”, Journal of Information and Optimization Sciences, vol. 42, no. 3, pp. 533-561 (2021). 
[19] S. M. Stefanov, Separable Optimization: Theory and Methods, Springer International Publishing, Springer Optimization and Its Applications, vol. 177, New York (2021). 
[20] S. M. Stefanov, “Numerical solution of systems of nonlinear equations defined by convex functions”, Journal of Interdisciplinary Mathematics, vol. 25, no. 4, pp. 951-962 (2022). 
[21] S. M. Stefanov, “On some properties of linear functionals”, Journal of Interdisciplinary Mathematics, vol. 25, no. 8, pp. 2491-2502 (2022). 
[22] S. M. Stefanov, “On the solution of quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 44, no. 2, pp. 243-253 (2023). 
[23] S. M. Stefanov, “Continuous linear knapsack problems revisited”, Journal of Information and Optimization Sciences, vol. 44, no. 5, pp. 909-922 (2023). 
[24] S. M. Stefanov, “Numerical solution of box constrained separable convex quadratic programming problems”, Journal of Information and Optimization Sciences, vol. 45, no. 1, pp. 57-71 (2024). 
[25] S. M. Stefanov, “Separable optimization: Approximation of the separable problem”, Journal of Statistics and Management Systems, submitted. 
[26] Hong-gang Xue, Cheng-xian Xu, and Feng-min Xu, “A branch and bound algorithm for separable concave programming”, Journal of Computational Mathematics, vol. 22, no. 6, pp. 895-904 (2004).

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