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Journal articles on the topic 'Programming (Mathematics) Convex programming'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Ceria, Sebastián, and João Soares. "Convex programming for disjunctive convex optimization." Mathematical Programming 86, no. 3 (December 1, 1999): 595–614. http://dx.doi.org/10.1007/s101070050106.

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2

Xu, Z. K., and S. C. Fang. "Unconstrained convex programming approach to linear programming." Journal of Optimization Theory and Applications 86, no. 3 (September 1995): 745–52. http://dx.doi.org/10.1007/bf02192167.

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3

fang, S. C., and H. S. J. Tsao. "An unconstrained convex programming approach to solving convex quadratic programming problems." Optimization 27, no. 3 (January 1993): 235–43. http://dx.doi.org/10.1080/02331939308843884.

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4

Fang, S. C. "An unconstrained convex programming view of linear programming." ZOR Zeitschrift f� Operations Research Methods and Models of Operations Research 36, no. 2 (March 1992): 149–61. http://dx.doi.org/10.1007/bf01417214.

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5

Kutateladze, S. S. "Variant of nontandard convex programming." Siberian Mathematical Journal 27, no. 4 (1987): 537–44. http://dx.doi.org/10.1007/bf00969166.

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6

Jeyakumar, V., and B. Mond. "On generalised convex mathematical programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 1 (July 1992): 43–53. http://dx.doi.org/10.1017/s0334270000007372.

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AbstractThe sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the funtion f and g satisfyfor some η: X0 × X0 → ℝnIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.

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7

Rajasekera, J. R., and S. C. Fang. "On the convex programming approach to linear programming." Operations Research Letters 10, no. 6 (August 1991): 309–12. http://dx.doi.org/10.1016/0167-6377(91)90001-6.

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8

Trujillo-Cortez, R., and S. Zlobec. "Bilevel convex programming models." Optimization 58, no. 8 (November 2009): 1009–28. http://dx.doi.org/10.1080/02331930701763330.

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9

Weir, T. "Programming with semilocally convex functions." Journal of Mathematical Analysis and Applications 168, no. 1 (July 1992): 1–12. http://dx.doi.org/10.1016/0022-247x(92)90185-g.

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10

Champion, T. "Duality gap in convex programming." Mathematical Programming 99, no. 3 (April 1, 2004): 487–98. http://dx.doi.org/10.1007/s10107-003-0461-z.

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11

Jeyakumar, V., D. T. Luc, and P. N. Tinh. "Convex composite non-Lipschitz programming." Mathematical Programming 92, no. 1 (March 1, 2002): 177–95. http://dx.doi.org/10.1007/s101070100274.

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12

Guerra, P. Jiménez, M. A. Melguizo, and M. J. Muñoz-Bouzo. "Sensitivity analysis in convex programming." Computers & Mathematics with Applications 58, no. 6 (September 2009): 1239–46. http://dx.doi.org/10.1016/j.camwa.2009.06.041.

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13

Thuy, Le Quang, Nguyen Thi Bach Kim, and Nguyen Tuan Thien. "Generating Efficient Outcome Points for Convex Multiobjective Programming Problems and Its Application to Convex Multiplicative Programming." Journal of Applied Mathematics 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/464832.

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Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

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14

Tseng, P. "Linearly constrained convex programming as unconstrained differentiable concave programming." Journal of Optimization Theory and Applications 85, no. 2 (May 1995): 489–94. http://dx.doi.org/10.1007/bf02192238.

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15

Shizheng, Li. "A constraint qualification for convex programming." Acta Mathematicae Applicatae Sinica 16, no. 4 (October 2000): 362–65. http://dx.doi.org/10.1007/bf02671125.

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16

Lahmdani, Anouar, and Mohamed Tifroute. "A smoothing sequential convex programming method." Applied Mathematical Sciences 15, no. 1 (2021): 33–45. http://dx.doi.org/10.12988/ams.2021.914344.

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17

Batagelj, Vladimir, Simona Korenjak-Černe, and Sandi Klavžar. "Dynamic programming and convex clustering." Algorithmica 11, no. 2 (February 1994): 93–103. http://dx.doi.org/10.1007/bf01182769.

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18

Mukherjee, R. N., and S. K. Mishra. "Multiobjective Programming with Semilocally Convex Functions." Journal of Mathematical Analysis and Applications 199, no. 2 (April 1996): 409–24. http://dx.doi.org/10.1006/jmaa.1996.0150.

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19

Jeyakumar, V., and X. Q. Yang. "Convex composite multi-objective nonsmooth programming." Mathematical Programming 59, no. 1-3 (March 1993): 325–43. http://dx.doi.org/10.1007/bf01581251.

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20

McCormick, Garth P., and Christoph Witzgall. "Logarithmic SUMT limits in convex programming." Mathematical Programming 90, no. 1 (March 2001): 113–45. http://dx.doi.org/10.1007/pl00011416.

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21

de Oliveira, Welington. "Sequential Difference-of-Convex Programming." Journal of Optimization Theory and Applications 186, no. 3 (August 4, 2020): 936–59. http://dx.doi.org/10.1007/s10957-020-01721-x.

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22

Mishra, S. K., and R. N. Mukherjee. "On generalised convex multi-objective nonsmooth programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 1 (July 1996): 140–48. http://dx.doi.org/10.1017/s0334270000000515.

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AbstractWe extend the concept of V-pseudo-invexity and V-quasi-invexity of multi-objective programming to the case of nonsmooth multi-objective programming problems. The generalised subgradient Kuhn-Tucker conditions are shown to be sufficient for a weak minimum of a multi-objective programming problem under certain assumptions. Duality results are also obtained.

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23

He, B., M. Tao, and X. Yuan. "A splitting method for separable convex programming." IMA Journal of Numerical Analysis 35, no. 1 (January 3, 2014): 394–426. http://dx.doi.org/10.1093/imanum/drt060.

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24

Zhou, XueGang, and JiHui Yang. "Global Optimization for the Sum of Concave-Convex Ratios Problem." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/879739.

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This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

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25

Yan, Zhaoxiang, and Shizheng Li. "A new class of generalized convex programming." Journal of Applied Mathematics and Computing 17, no. 1-2 (March 2005): 351–60. http://dx.doi.org/10.1007/bf02936061.

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26

Jarre, Florian. "Interior-point methods for convex programming." Applied Mathematics & Optimization 26, no. 3 (November 1992): 287–311. http://dx.doi.org/10.1007/bf01371086.

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27

Egudo, R. R., T. Weir, and B. Mond. "Duality without constraint qualification for multiobjective programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 33, no. 4 (April 1992): 531–44. http://dx.doi.org/10.1017/s0334270000007219.

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AbstractExtending earlier duality results for multiobjective programs, this paper defines dual problems for convex and generalised convex multiobjective programs without requiring a constraint qualification. The duals provide multiobjective extensions of the classical duals of Wolfe and Schechter and some of the more recent duals of Mond and Weir.

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28

Levitin, E. S. "Investigation of some parametric convex programming problems." Computational Mathematics and Modeling 3, no. 4 (1992): 402–9. http://dx.doi.org/10.1007/bf01133068.

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29

Oliveira, Rúbia M., and Paulo A. V. Ferreira. "A convex analysis approach for convex multiplicative programming." Journal of Global Optimization 41, no. 4 (December 21, 2007): 579–92. http://dx.doi.org/10.1007/s10898-007-9267-5.

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30

Jung, Jin Hyuk, Dianne P. O’Leary, and André L. Tits. "Adaptive constraint reduction for convex quadratic programming." Computational Optimization and Applications 51, no. 1 (March 9, 2010): 125–57. http://dx.doi.org/10.1007/s10589-010-9324-8.

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31

Fukushima, Masao, Mounir Haddou, Hien Van Nguyen, Jean-Jacques Strodiot, Takanobu Sugimoto, and Eiki Yamakawa. "A parallel descent algorithm for convex programming." Computational Optimization and Applications 5, no. 1 (January 1996): 5–37. http://dx.doi.org/10.1007/bf00429749.

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32

Shvartsman, Ilya. "On stability of minimizers in convex programming." Nonlinear Analysis: Theory, Methods & Applications 75, no. 3 (February 2012): 1563–71. http://dx.doi.org/10.1016/j.na.2011.03.033.

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33

Henrion, R., and T. Surowiec. "On calmness conditions in convex bilevel programming." Applicable Analysis 90, no. 6 (June 2011): 951–70. http://dx.doi.org/10.1080/00036811.2010.495339.

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34

Lewis, A. S. "Facial reduction in partially finite convex programming." Mathematical Programming 65, no. 1-3 (February 1994): 123–38. http://dx.doi.org/10.1007/bf01581693.

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35

Zhou, X., F. Sharifi Mokhtarian, and S. Zlobec. "A simple constraint qualification in convex programming." Mathematical Programming 61, no. 1-3 (August 1993): 385–97. http://dx.doi.org/10.1007/bf01582159.

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36

Iusem, Alfredo N., and B. F. Svaiter. "A row-action method for convex programming." Mathematical Programming 64, no. 1-3 (March 1994): 149–71. http://dx.doi.org/10.1007/bf01582569.

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37

Emama, Tarek. "Optimality for E-[0,1] convex multi-objective programming." Filomat 31, no. 3 (2017): 529–41. http://dx.doi.org/10.2298/fil1703529e.

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In this paper, we interest with deriving the sufficient and necessary conditions for optimal solution of special classes of Programming. These classes involve generalized E-[0,1] convex functions. Characterization of efficient solutions for E-[0,1] convex multi-objective Programming are obtained. Finally, sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are derived.

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38

Chan, Timothy M. "Deterministic Algorithms for 2-d Convex Programming and 3-d Online Linear Programming." Journal of Algorithms 27, no. 1 (April 1998): 147–66. http://dx.doi.org/10.1006/jagm.1997.0914.

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39

Asgharian, M., and S. Zlobec. "Convex Parametric Programming in Abstract Spaces." Optimization 51, no. 6 (August 2002): 841–61. http://dx.doi.org/10.1080/0233193021000015659.

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40

Craven, B. D., D. Ralph, and B. M. Glover. "Small convex-valued subdifferentials in mathematical programming." Optimization 32, no. 1 (January 1995): 1–21. http://dx.doi.org/10.1080/02331939508844032.

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41

Mu, Xuewen, and Yaling Zhang. "An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/379734.

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An alternating direction method is proposed for convex quadratic second-order cone programming problems with bounded constraints. In the algorithm, the primal problem is equivalent to a separate structure convex quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

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42

Özöğür‐Akyüz, Süreyya, Buse Çisil Otar, and Pınar Karadayı Atas. "Ensemble cluster pruning via convex‐concave programming." Computational Intelligence 36, no. 1 (January 5, 2020): 297–319. http://dx.doi.org/10.1111/coin.12267.

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43

Jansson, Christian. "On verified numerical computations in convex programming." Japan Journal of Industrial and Applied Mathematics 26, no. 2-3 (October 2009): 337–63. http://dx.doi.org/10.1007/bf03186539.

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44

Fu, J. Y., and Y. H. Wang. "Arcwise Connected Cone-Convex Functions and Mathematical Programming." Journal of Optimization Theory and Applications 118, no. 2 (August 2003): 339–52. http://dx.doi.org/10.1023/a:1025451422581.

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45

Fan, Xiaona, and Bo Yu. "A polynomial path following algorithm for convex programming." Applied Mathematics and Computation 196, no. 2 (March 2008): 866–78. http://dx.doi.org/10.1016/j.amc.2007.07.021.

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46

Weir, T., and V. Jeyakumar. "A class of nonconvex functions and mathematical programming." Bulletin of the Australian Mathematical Society 38, no. 2 (October 1988): 177–89. http://dx.doi.org/10.1017/s0004972700027441.

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A class of functions, called pre-invex, is defined. These functions are more general than convex functions and when differentiable are invex. Optimality conditions and duality theorems are given for both scalar-valued and vector-valued programs involving pre-invex functions.

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47

Preda, Vasile. "On nonlinear programming and matrix game equivalence." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 35, no. 4 (April 1994): 429–38. http://dx.doi.org/10.1017/s0334270000009528.

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AbstractIn the framework of Mond-Weir duality a new equivalence between nonlinear programming and a matrix game is given. Finally, certain conclusions about convex programming with nested maxima and matrix games are also included.

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48

Carlone, L., V. Srivastava, F. Bullo, and G. C. Calafiore. "Distributed Random Convex Programming via Constraints Consensus." SIAM Journal on Control and Optimization 52, no. 1 (January 2014): 629–62. http://dx.doi.org/10.1137/120885796.

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49

Alvarez, Felipe, Jérôme Bolte, and Olivier Brahic. "Hessian Riemannian Gradient Flows in Convex Programming." SIAM Journal on Control and Optimization 43, no. 2 (January 2004): 477–501. http://dx.doi.org/10.1137/s0363012902419977.

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50

Glazos, Michael P., Stefen Hui, and Stanislaw H. Zak. "Sliding Modes in Solving Convex Programming Problems." SIAM Journal on Control and Optimization 36, no. 2 (March 1998): 680–97. http://dx.doi.org/10.1137/s0363012993255880.

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