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Journal articles on the topic 'Nonconvex programming'

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Published: 4 June 2021
Last updated: 31 January 2023

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1

Falk, James E., and Ferenc Forgo. "Nonconvex Programming." Mathematics of Computation 53, no. 187 (July 1989): 449. http://dx.doi.org/10.2307/2008379.

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2

Mukai, Hiro. "Nonconvex programming." European Journal of Operational Research 42, no. 1 (September 1989): 105–6. http://dx.doi.org/10.1016/0377-2217(89)90064-7.

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3

Jiao, Hongwei, and Yongqiang Chen. "A Global Optimization Algorithm for Generalized Quadratic Programming." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/215312.

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We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.
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4

Scholtes, Stefan. "Nonconvex Structures in Nonlinear Programming." Operations Research 52, no. 3 (June 2004): 368–83. http://dx.doi.org/10.1287/opre.1030.0102.

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5

Pardalos, Panos M., and G. M. Guisewite. "Parallel computing in nonconvex programming." Annals of Operations Research 43, no. 2 (February 1993): 87–107. http://dx.doi.org/10.1007/bf02024487.

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6

Antczak, Tadeusz. "Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Ф,ρ)-V-invexity and generalized (Ф,ρ)-V-invexity." Filomat 30, no. 14 (2016): 3649–65. http://dx.doi.org/10.2298/fil1614649a.

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A new class of nonconvex smooth semi-infinite multiobjective fractional programming problems with both inequality and equality constraints is considered. We formulate and establish several parametric sufficient optimality conditions for efficient solutions in such nonconvex vector optimization problems under (?,?)-V-invexity and/or generalized (?,?)-V-invexity hypotheses. With the reference to the said functions, we extend some results of efficiency for a larger class of nonconvex smooth semi-infinite multiobjective programming problems in comparison to those ones previously established in the literature under other generalized convexity notions. Namely, we prove the sufficient optimality conditions for such nonconvex semi-infinite multiobjective fractional programming problems in which not all functions constituting them have the fundamental property of convexity, invexity and most generalized convexity notions.
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7

KUMAR, NARENDER, R. K. BUDHRAJA, and APARNA MEHRA. "APPROXIMATE EFFICIENCY FOR n-SET MULTIOBJECTIVE FRACTIONAL PROGRAMMING." Asia-Pacific Journal of Operational Research 21, no. 02 (June 2004): 197–206. http://dx.doi.org/10.1142/s0217595904000199.

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In this paper, we introduce new concepts of ε-weak efficient solutions and ε-efficient solutions for a nonconvex multiobjective fractional programming problem involving n-set functions. Using an ε-parametric approach and a new theorem of alternative for nonconvex n-set functions, some necessary and sufficient conditions for ε-approximate solutions are derived
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8

Moloshnyuk, A. N. "A duality relation in nonconvex programming." Journal of Soviet Mathematics 41, no. 3 (May 1988): 1050–53. http://dx.doi.org/10.1007/bf01103261.

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9

Forsgren, Anders. "Optimality conditions for nonconvex semidefinite programming." Mathematical Programming 88, no. 1 (June 2000): 105–28. http://dx.doi.org/10.1007/pl00011370.

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10

Antczak, Tadeusz. "Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity." Filomat 31, no. 9 (2017): 2557–74. http://dx.doi.org/10.2298/fil1709557a.

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Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.
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11

Chen, Jieqiu, and Samuel Burer. "Globally solving nonconvex quadratic programming problems via completely positive programming." Mathematical Programming Computation 4, no. 1 (November 16, 2011): 33–52. http://dx.doi.org/10.1007/s12532-011-0033-9.

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12

Zhang, Liwei, Yang Li, and Jia Wu. "Nonlinear rescaling Lagrangians for nonconvex semidefinite programming." Optimization 63, no. 6 (October 28, 2013): 899–920. http://dx.doi.org/10.1080/02331934.2013.848861.

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13

Burer, Samuel, and Adam N. Letchford. "On Nonconvex Quadratic Programming with Box Constraints." SIAM Journal on Optimization 20, no. 2 (January 2009): 1073–89. http://dx.doi.org/10.1137/080729529.

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14

Loridan, P. "?-Duality theorem of nondifferentiable nonconvex multiobjective programming." Journal of Optimization Theory and Applications 74, no. 3 (September 1992): 565–66. http://dx.doi.org/10.1007/bf00940327.

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15

Liu, J. C. "?-Duality theorem of nondifferentiable nonconvex multiobjective programming." Journal of Optimization Theory and Applications 74, no. 3 (September 1992): 567–68. http://dx.doi.org/10.1007/bf00940328.

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16

Liu, J. C. "?-duality theorem of nondifferentiable nonconvex multiobjective programming." Journal of Optimization Theory and Applications 69, no. 1 (April 1991): 153–67. http://dx.doi.org/10.1007/bf00940466.

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17

Sherali, Hanif D., and Hongjie Wang. "Global optimization of nonconvex factorable programming problems." Mathematical Programming 89, no. 3 (February 2001): 459–78. http://dx.doi.org/10.1007/pl00011409.

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18

Bartels, Sören, and Tomáš Roubíček. "Linear-programming approach to nonconvex variational problems." Numerische Mathematik 99, no. 2 (November 9, 2004): 251–87. http://dx.doi.org/10.1007/s00211-004-0549-2.

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19

Keller, André A. "Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (August 1, 2015): 129–43. http://dx.doi.org/10.1515/jmbm-2015-0015.

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AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are replaced by new numerous pairwise products of the constraints. In the linearization phase, each distinct quadratic term is replaced by a single new RLT variable. This RLT process produces an LP relaxation. The LP-RLT yieds a lower bound on the global minimum. LMI formulations (linear matrix inequalities) have been proposed to treat efficiently with nonconvex sets. An LMI is equivalent to a system of polynomial inequalities. A semialgebraic convex set describes the system. The feasible sets are spectrahedra with curved faces, contrary to the LP case with polyhedra. Successive LMI relaxations of increasing size yield the global optimum. Nonlinear inequalities are converted to an LMI form using Schur complements. Optimizing a nonconvex polynomial is equivalent to the LP over a convex set. Engineering application interests include system analysis, control theory, combinatorial optimization, statistics, and structural design optimization.
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20

Scott, Carlton H., and Thomas R. Jefferson. "Duality for linear multiplicative programs." ANZIAM Journal 46, no. 3 (January 2005): 393–97. http://dx.doi.org/10.1017/s1446181100008336.

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AbstractLinear multiplicative programs are an important class of nonconvex optimisation problems that are currently the subject of considerable research as regards the development of computational algorithms. In this paper, we show that mathematical programs of this nature are, in fact, a special case of more general signomial programming, which in turn implies that research on this latter problem may be valuable in analysing and solving linear multiplicative programs. In particular, we use signomial programming duality theory to establish a dual program for a nonconvex linear multiplicative program. An interpretation of the dual variables is given.
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21

Zhou, Xue-Gang, and Bing-Yuan Cao. "A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/697321.

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A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function witheas the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.
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22

Li, Guoquan, and Yan Wang. "Global Optimality Conditions for Nonlinear Programming Problems with Linear Equality Constraints." Journal of Applied Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/213178.

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Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In particular, global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. Some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them.
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23

Phan, Duy Nhat, Hoai An Le Thi, and Tao Pham Dinh. "Sparse Covariance Matrix Estimation by DCA-Based Algorithms." Neural Computation 29, no. 11 (November 2017): 3040–77. http://dx.doi.org/10.1162/neco_a_01012.

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This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.
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24

Lu, Yuan, Wei Wang, Li-Ping Pang, and Dan Li. "A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/376403.

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A class of constrained nonsmooth nonconvex optimization problems, that is, piecewiseC2objectives with smooth inequality constraints are discussed in this paper. Based on the𝒱𝒰-theory, a superlinear convergent𝒱𝒰-algorithm, which uses a nonconvex redistributed proximal bundle subroutine, is designed to solve these optimization problems. An illustrative example is given to show how this convergent method works on a Second-Order Cone programming problem.
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25

Shen, Xiaodong, Yang Liu, and Yan Liu. "A Multistage Solution Approach for Dynamic Reactive Power Optimization Based on Interval Uncertainty." Mathematical Problems in Engineering 2018 (October 18, 2018): 1–10. http://dx.doi.org/10.1155/2018/3854812.

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In order to solve the uncertainty and randomness of the output of the renewable energy resources and the load fluctuations in the reactive power optimization, this paper presents a novel approach focusing on dealing with the issues aforementioned in dynamic reactive power optimization (DRPO). The DRPO with large amounts of renewable resources can be presented by two determinate large-scale mixed integer nonlinear nonconvex programming problems using the theory of direct interval matching and the selection of the extreme value intervals. However, it has been admitted that the large-scale mixed integer nonlinear nonconvex programming is quite difficult to solve. Therefore, in order to simplify the solution, the heuristic search and variable correction approaches are employed to relax the nonconvex power flow equations to obtain a mixed integer quadratic programming model which can be solved using software packages such as CPLEX and GUROBI. The ultimate solution and the performance of the presented approach are compared to the traditional methods based on the evaluations using IEEE 14-, 118-, and 300-bus systems. The experimental results show the effectiveness of the presented approach, which potentially can be a significant tool in DRPO research.
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26

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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27

Ye, Yinyu. "On affine scaling algorithms for nonconvex quadratic programming." Mathematical Programming 56, no. 1-3 (August 1992): 285–300. http://dx.doi.org/10.1007/bf01580903.

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28

Garcés, Rodrigo, Walter Gómez, and Florian Jarre. "A self-concordance property for nonconvex semidefinite programming." Mathematical Methods of Operations Research 74, no. 1 (March 30, 2011): 77–92. http://dx.doi.org/10.1007/s00186-011-0350-9.

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29

Forsgren, Anders, and Philip E. Gill. "Primal-Dual Interior Methods for Nonconvex Nonlinear Programming." SIAM Journal on Optimization 8, no. 4 (November 1998): 1132–52. http://dx.doi.org/10.1137/s1052623496305560.

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30

Xiao, Y., H. J. Xiong, and B. Yu. "Truncated aggregate homotopy method for nonconvex nonlinear programming." Optimization Methods and Software 29, no. 1 (March 4, 2013): 160–76. http://dx.doi.org/10.1080/10556788.2012.762365.

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31

Mráz, F. "Local minimizer of a nonconvex quadratic programming problem." Computing 45, no. 3 (September 1990): 283–89. http://dx.doi.org/10.1007/bf02250640.

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32

Guerra-Vázquez, Francisco, Jan-J. Rückmann, and Ralf Werner. "On saddle points in nonconvex semi-infinite programming." Journal of Global Optimization 54, no. 3 (July 27, 2011): 433–47. http://dx.doi.org/10.1007/s10898-011-9753-7.

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33

Sherali, Hanif D., Evrim Dalkiran, and Leo Liberti. "Reduced RLT representations for nonconvex polynomial programming problems." Journal of Global Optimization 52, no. 3 (July 31, 2011): 447–69. http://dx.doi.org/10.1007/s10898-011-9757-3.

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34

Kaul, R. N., and Surjeet Kaur. "Optimality criteria in nonlinear programming involving nonconvex functions." Journal of Mathematical Analysis and Applications 105, no. 1 (January 1985): 104–12. http://dx.doi.org/10.1016/0022-247x(85)90099-x.

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35

ANTCZAK, TADEUSZ. "THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS." Asia-Pacific Journal of Operational Research 27, no. 05 (October 2010): 559–76. http://dx.doi.org/10.1142/s0217595910002855.

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In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.
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36

Hong, Tao, and Geng-xin Zhang. "Power Allocation for Reducing PAPR of Artificial-Noise-Aided Secure Communication System." Mobile Information Systems 2020 (July 18, 2020): 1–15. http://dx.doi.org/10.1155/2020/6203079.

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The research of improving the secrecy capacity (SC) of wireless communication system using artificial noise (AN) is one of the classic models in the field of physical layer security communication. In this paper, we consider the peak-to-average power ratio (PAPR) problem in this AN-aided model. A power allocation algorithm for AN subspaces is proposed to solve the nonconvex optimization problem of PAPR. This algorithm utilizes a series of convex optimization problems to relax the nonconvex optimization problem in a convex way based on fractional programming, difference of convex (DC) functions programming, and nonconvex quadratic equality constraint relaxation. Furthermore, we also derive the SC of the proposed signal under the condition of the AN-aided model with a finite alphabet and the nonlinear high-power amplifiers (HPAs). Simulation results show that the proposed algorithm reduces the PAPR value of transmit signal to improve the efficiency of HPA compared with benchmark AN-aided secure communication signals in the multiple-input single-output (MISO) model.
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37

Weir, T., and B. Mond. "Proper efficiency and duality for vector valued optimization problems." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (August 1987): 21–34. http://dx.doi.org/10.1017/s1446788700028937.

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AbstractThe duality results of Wolfe for scalar convex programming problems and some of the more recent duality results for scalar nonconvex programming problems are extended to vector valued programs. Weak duality is established using a ‘Pareto’ type relation between the primal and dual objective functions.
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38

SAKAWA, Masatoshi, Ichiro NISHIZAKI, Yoshio UEMURA, and Masatoshi HITAKA. "Interactive Fuzzy Programming for Multi-Level Nonconvex Nonlinear Programming Problems through Genetic Algorithms." Journal of Japan Society for Fuzzy Theory and Systems 12, no. 2 (2000): 304–12. http://dx.doi.org/10.3156/jfuzzy.12.2_96.

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39

Bonami, Pierre, Oktay Günlük, and Jeff Linderoth. "Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods." Mathematical Programming Computation 10, no. 3 (February 24, 2018): 333–82. http://dx.doi.org/10.1007/s12532-018-0133-x.

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40

Anstreicher, Kurt M. "Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming." Journal of Global Optimization 43, no. 2-3 (November 7, 2008): 471–84. http://dx.doi.org/10.1007/s10898-008-9372-0.

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41

Sakawa, Masatoshi, Ichiro Nishizaki, Yoshio Uemura, and Masatoshi Hitaka. "Interactive fuzzy programming for two-level nonconvex nonlinear programming problems through genetic algorithms." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 84, no. 3 (2000): 33–41. http://dx.doi.org/10.1002/1520-6440(200103)84:3<33::aid-ecjc4>3.0.co;2-d.

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42

Corstjens, Marcel, and Peter Doyle. "The Application of Geometric Programming to Marketing Problems." Journal of Marketing 49, no. 1 (January 1985): 137–44. http://dx.doi.org/10.1177/002224298504900113.

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Geometric programming (GP) is a new technique that appears to have significant potential in marketing. Researchers have avoided optimization models in marketing, partially because empirical estimates of typical marketing response functions suggest nonconvex maximization problems not easily handled by conventional nonlinear programming. GP now offers a convenient structure for modeling and optimizing the realistic complexity of many important marketing problems.
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43

Ahmadian, Ali, and Reza Afsharinaf. "An Approximation Method for Solving Nonconvex Quadratic Programming Problems." Journal of Applied Sciences 11, no. 23 (November 15, 2011): 3807–10. http://dx.doi.org/10.3923/jas.2011.3807.3810.

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44

Le Thi, Hoai An, Van Ngai Huynh, Tao Pham Dinh, and Hoang Phuc Hau Luu. "Stochastic Difference-of-Convex-Functions Algorithms for Nonconvex Programming." SIAM Journal on Optimization 32, no. 3 (September 2022): 2263–93. http://dx.doi.org/10.1137/20m1385706.

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45

Chen, Xiaojun, Lei Guo, Zhaosong Lu, and Jane J. Ye. "An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming." SIAM Journal on Numerical Analysis 55, no. 1 (January 2017): 168–93. http://dx.doi.org/10.1137/15m1052834.

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46

Dong, Li, Bo Yu, and Guohui Zhao. "A spline smoothing homotopy method for nonconvex nonlinear programming." Optimization 65, no. 4 (July 13, 2015): 729–49. http://dx.doi.org/10.1080/02331934.2015.1064122.

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47

Yu, Bo, Guo-chen Feng, and Shao-Liang Zhang. "The aggregate constraint homotopy method for nonconvex nonlinear programming." Nonlinear Analysis: Theory, Methods & Applications 45, no. 7 (September 2001): 839–47. http://dx.doi.org/10.1016/s0362-546x(99)00420-4.

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48

Li, Han-Lin, and Chian-Son Yu. "A global optimization method for nonconvex separable programming problems." European Journal of Operational Research 117, no. 2 (September 1999): 275–92. http://dx.doi.org/10.1016/s0377-2217(98)00243-4.

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49

Nobakhtian, Soghra, and Narjes Shafiei. "A Benson type algorithm for nonconvex multiobjective programming problems." TOP 25, no. 2 (August 23, 2016): 271–87. http://dx.doi.org/10.1007/s11750-016-0430-3.

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50

Ghadimi, Saeed, and Guanghui Lan. "Accelerated gradient methods for nonconvex nonlinear and stochastic programming." Mathematical Programming 156, no. 1-2 (February 21, 2015): 59–99. http://dx.doi.org/10.1007/s10107-015-0871-8.

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