Cited by 744Advanced Optimization Algorithms ResearchOptimization and Variational AnalysisComplexity and Algorithms in Graphs

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Variations and extension of the convex–concave procedure

Lipp, Thomas, Boyd, Stephen·2016·Optimization and Engineering

Overview

Integrity signals

Registry

Crossref · 10.1007/s11081-015-9294-x

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Although the objective converges in all cases, it does not necessarily converge to a local minimum (Lipp & Boyd, 2016).

    “Although the objective converges in all cases, it does not necessarily converge to a local minimum (Lipp & Boyd, 2016).”

    From Hopfield Networks is All You Need (2020) · cites this paper as Lipp & Boyd, 2016

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 92

  1. Absil PA, Mahony R, Sepulchre R (2009) Optimization algorithms on matrix manifolds. Princeton University Press, Princeton
  2. Agin N (1966) Optimum seeking with branch and bound. Manag Sci 13:176–185 · DOI
  3. Beck A, Ben-Tal A, Tetrushvili L (2010) A sequential parametric convex approximation method with applications to nonconvex truss topology design problems. J Glob Optim 47(1):29–51 · DOI
  4. Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396 · DOI
  5. Boggs PT, Tolle JW (1995) Sequential quadratic programming. Acta Numer 4(1):1–51 · DOI · Paper page
  6. Boyd S, Vandenberghe L (2004) Convex Optim. Cambridge University Press, Cambridge · DOI · Paper page
  7. Boyd S, Hast M, Åström KJ (2015) MIMO PID tuning via iterated LMI restriction. Int J Robust Nonlinear Control To appear · DOI
  8. Byrd RH, Gilbert JC, Nocedal J (2000) A trust region method based on interior point techniques for nonlinear programming. Math Program 89(1):149–185 · DOI
  9. Byrne C (2000) Block-iterative interior point optimization methods for image reconstruction from limited data. Inverse Probl 16(5):1405 · DOI
  10. Crawford JM, Auton LD (1996) Experimental results on the crossover point in random 3-SAT. Artif Intell 81(1):31–57 · DOI
  11. De Leeuw J (1977) Applications of convex analysis to multidimensional scaling. In: Barra JR, Brodeau F, Romier G, Van Cutsem B (eds) Recent developments in statistics. North Holland Publishing, Amsterdam, pp 133–146
  12. Di Pillo G, Grippo L (1989) Exact penalty functions in constrained optimization. SIAM J Control Optim 27(6):1333–1360 · DOI
  13. Domahidi A, Chu E, Boyd S (2013) ECOS: an SOCP solver for embedded systems. In: European control conference, pp 3071–3076 · DOI
  14. Drira A, Pierreval H, Hajri-Gabouh S (2007) Facility layout problems: a survey. Annu Rev Control 31(2):255–267 · DOI
  15. du Merle O, Villeneuve D, Desrosiers J, Hansen P (1999) Stabilized column generation. Discret Math 194(1):229–237 · DOI
  16. Edelman A, Tomás AA, Smith TS (1998) The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl 20(2):303–353 · DOI
  17. Elzinga J, Moore TJ (1975) A central cutting plane algorithm for convex programming problems. Math Program 8:134–145 · DOI
  18. Falk JE, Hoffmann KR (1976) A successive underestimation method for concave minimization problems. Math Oper Res 1(3):251–259 · DOI
  19. Falk JE, Soland RM (1969) An algorithm for separable nonconvex programming problems. Manag Sci 15(9):550–569 · DOI
  20. Fardad M, Jovanović MR (2014) On the design of optimal structured and sparse feedback gains via sequential convex programming. In: American control conference, pp 2426–2431 · DOI
  21. Garcia Palomares UM, Mangasarian OL (1976) Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems. Math Program 11(1):1–13 · DOI
  22. Gill PE, Wong E (2012) Sequential quadratic programming methods. In: Mixed integer nonlinear programming, Springer, pp 147–224 · DOI
  23. Grant M, Boyd S (2008) Graph implementation for nonsmooth convex programs. In: Blondel V, Boyd S, Kimura H (eds) Recent Advances in learning and control, lecture notes in control and information sciences, Springer. http://stanford.edu/ boyd/graph_dcp.html · DOI
  24. Han SP, Mangasarian OL (1979) Exact penalty functions in nonlinear programming. Math Program 17(1):251–269 · DOI
  25. Hanan M, Kurtzberg J (1972) Placement techniques. In: Breuer MA (ed) Design automation of digital systems, vol 1. Prentice-Hall, Upper Saddle River, pp 213–282
  26. Hartman P (1959) On functions representable as a difference of convex functions. Pac J Math 9(3):707–713 · DOI
  27. Hillestad RJ (1975) Optimization problems subject to a budget constraint with economies of scale. Oper Res 23(6):1091–1098 · DOI
  28. Hillestad RJ, Jacobsen SE (1980a) Linear programs with an additional reverse convex constraint. Appl Math Optim 6(1):257–269 · DOI
  29. Hillestad RJ, Jacobsen SE (1980b) Reverse convex programming. Appl Math Optim 6(1):63–78 · DOI
  30. Horst R (1986) A general class of branch-and-bound methods in global optimization with some new approaches for concave minimization. J Optim Theory Appl 51(2):271–291 · DOI
  31. Horst R, Thoai NV (1999) DC programming: overview. J Optim Theory Appl 103(1):1–43 · DOI
  32. Horst R, Tuy H (1996) Global Optimization, 3rd edn. Springer, New York · DOI
  33. Horst R, Phong TQ, Thoai NV, De Vries J (1991a) On solving a DC programming problem by a sequence of linear programs. J Glob Optim 1(2):183–203 · DOI
  34. Horst R, Thoai NV, Benson HP (1991b) Concave minimization via conical partitions and polyhedral outer approximation. Math Program 50:259–274 · DOI
  35. Horst R, Pardalos PM, Thoai NV (1995) Introduction to global optimization. Kluwer Academic Publishers, Dordrecht
  36. Karp RM (1972) Reducibility among combinatorial problems. In: Thatcher JW, Miller RE (eds) Complexity of computer computation. Plenum, Berlin, pp 85–104 · DOI · Paper page
  37. Kelly JE Jr (1960) The cutting-plane method for solving convex programs. J Soc Ind Appl Math 8(4):703–712 · DOI
  38. Lanckreit GR, Sriperumbudur BK (2009) On the convergence of the concave-convex procedure. Adv Neural Inf Process Syst, 1759–1767
  39. Lange K (2004) Optimization. Springer texts in statistics. Springer, New York
  40. Lange K, Hunter DR, Yang I (2000) Optimization transfer using surrogate objective functions. J Comput Graph Stat 9(1):1–20 · DOI
  41. Lawler EL, Wood DE (1966) Branch-and-bound methods: a survey. Oper Res 14:699–719 · DOI
  42. Le HM, Le Thi HA, Pham Dinh T, Bouvry P (2010) A combined DCA: GA for constructing highly nonlinear balanced Boolean functions in cryptography. J Glob Optim 47(4):597–613 · DOI
  43. Le Thi HA (2003) Solving large scale molecular distance geometry problems by a smoothing technique via the Gaussian transform and DC programming. J Glob Optim 27(4):375–397 · DOI
  44. Le Thi HA, Pham Dinh T (1997) Solving a class of linearly constrainted indefinite quadratic problems by DC algorithms. J Glob Optim 11(3):253–285 · DOI
  45. Le Thi HA, Pham Dinh T (2003) Large-scale molecular optimization for distance matrices by a DC optimization approach. SIAM J Optim 14(1):77–114 · DOI
  46. Le Thi HA, Pham Dinh T (2008) A continuous approach for the concave cost supply problem via DC programming and DCA. Discret Appl Math 156(3):325–338 · DOI
  47. Le Thi HA, Pham Dinh T, Muu LD (1996) Numerical solution for optimization over the efficient set by d.c. optimization algorithms. Oper Res Lett 19:117–128 · DOI
  48. Le Thi HA, Pham Dinh T, Muu LD (1998) A combined D.C. optimization-ellipsoidal branch-and-bound algorithm for solving nonconvex quadratic programming problems. J Comb Optim 2(1):9–28 · DOI
  49. Le Thi HA, Pham Dinh T, Thoai NV (2002) Combination between global and local methods for solving an optimization problem over the efficient set. Eur J Oper Res 142(2):258–270 · DOI
  50. Le Thi HA, Moeini M, Pham Dinh T (2009a) DC programming approach for portfolio optimization under step increasing transaction costs. Optimization 58(3):267–289 · DOI
  51. Le Thi HA, Pham Dinh T, Nguyen CN, Thoai NV (2009b) DC programming techniques for solving a class of nonlinear bilevel programs. J Glob Optim 44(3):313–337 · DOI
  52. Le Thi HA, Pham Dinh T, Ngai HV (2012) Exact penalty and error bounds in DC programming. J Glob Optim 52(3):509–535 · DOI
  53. Le Thi HA, Huynh VN, Pham Dinh T (2014) DC programming and DCA for general DC programs. Adv Comput Methods Knowl Eng, 15–35 · DOI
  54. Little RJA, Rubin DB (1987) Statistical analysis with missing data. Wiley, New York
  55. Maranas CD, Floudas CA (1997) Global optimization in generalized geometric programming. Comput Chem Eng 21(4):351–369 · DOI
  56. McLachlan G, Krishnan T (2007) The EM algorithm and extensions. Wiley, Hoboken
  57. Meyer R (1970) The validity of a family of optimization methods. SIAM J Control 8(1):41–54 · DOI
  58. Mitchell D, Selman B, Levesque H (1992) Hard and easy distributions and SAT problems. Proc Tenth Natl Conf Artif Intell 92:459–465
  59. Mueller JB, Larsson R (2008) Collision avoidance maneuver planning with robust optimization. In: International ESA conference on guidance, navigation and control systems, Tralee · DOI
  60. Mutapcic A, Boyd S (2009) Cutting-set methods for robust convex optimization with pessimizing oracles. Optim Methods Softw 24(3):381–406 · DOI
  61. Muu LD (1985) A convergent algorithm for solving linear programs with an additional reverse convex constraint. Kybernetika 21(6):428–435
  62. Naghsh MM, Modarres-Hashemi M, ShahbazPanahi S, Soltanalian M, Stoica P (2013) Unified optimization framework for multi-static radar code design using information-theoretic criteria. IEEE Trans Signal Process 61(21):5401–5416 · DOI
  63. Nam GJ, Cong J (eds) (2007) Modern circuit placement. Springer, New York
  64. Ndiaye BM, Pham Dinh T, Le Thi HA (2012) DC programming and DCA for large-scale two-dimensional packing problems. Springer, New York · DOI
  65. Niu YS, Pham Dinh T (2014) DC programming approaches for BMI and QMI feasibility problems. Adv Comput Methods Knowl Eng 6:37–63 · DOI
  66. Nocedal J, Wright SJ (2006) Numerical optimization. Springer, New York
  67. Pham Dinh T, Le Thi HA (1997) Convex analysis approach to DC programming: theory, algorithms, and applications. Acta Math Vietnam 22(1):289–355
  68. Pham Dinh T, Le Thi HA (1998) A DC optimization algorithm for solving the trust-region subproblem. SIAM J Optim 8(2):476–505 · DOI
  69. Pham Dinh T, Le Thi HA (2014) Recent advances in DC programming and DCA. Trans Comput Intell XIII 13:1–37 · DOI
  70. Pham Dinh T, Souad EB (1986) Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients. In: Hiriart-Urruty JB (ed) FERMAT Days 85: mathematics for optimization. Elsevier Scince Publishers B. V., Amsterdam, pp 249–271
  71. Pham Dinh T, Le Thi HA, Akoa F (2008) Combining DCA (DC algorithms) and interior point techniques for large-scale nonconvex quadratic programming. Optim Methods Softw 23(4):609–629 · DOI
  72. Pham Dinh T, Nguyen CN, Le Thi HA (2010) An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs. J Glob Optim 48(4):595–632 · DOI
  73. Powell MJD (1978) A fast algorithm for nonlinearly constrained optimization calculations. Springer, New York, pp 144–157
  74. Robinson SM (1972) A quadratically-convergent algorithm for general nonlinear programming problems. Math Program 3(1):145–156 · DOI
  75. Shulman J, Ho J, Lee A, Awwal I, Bradlow H, Abbeel P (2013) Finding locally optimal, collision-free trajectories with sequential convex optimization. In: Robotics: science and systems, vol 9. pp 1–10 · DOI
  76. Singh SP, Sharma RRK (2006) A review of different approaches to the facility layout problems. Int J Adv Manuf Technol 30(5):425–433 · DOI
  77. Smola AJ, Vishwanathan SVN, Hofmann T (2005) Kernel methods for missing variables. In: Proceedings of 10th international workshop on artificial intelligence and statistics
  78. Soland RM (1971) An algorithm for separable nonconvex programming problems II: nonconvex constraints. Manag Sci 17(11):759–773 · DOI
  79. Stoica P, Babu P (2012) SPICE and LIKES: two hyperparameter-free methods for sparse-parameter estimation. Signal Process 92(8):1580–1590 · DOI
  80. Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373 · DOI
  81. Thoai NV, Tuy H (1980) Convergent algorithms for minimizing a concave function. Math Oper Res 5(4):556–566 · DOI
  82. Toh KC, Todd MJ, Tutuncu RH (1999) SDPT3—a MATLAB software package for semidefinite programming. Optim Methods Softw 11:545–581 · DOI
  83. Tutuncu RH, Toh KC, Todd MJ (2003) Solving semidfinite-quadratic-linear programs using SDPT3. Math Program 95(2):189–217 · DOI
  84. Tuy H (1983) On outer approximation methods for solving concave minimization problems. Acta Math Vietnam 8(2):3–34
  85. Tuy H (1986) A general deterministic approach to global optimization via D.C. programming. N-Holl Math Stud 129:273–303 · DOI
  86. Tuy H, Horst R (1988) Convergence and restart in branch-and-bound algorithms for global optimization. Applications to concave minimization and DC optimization problems. Math Program 41(2):161–183 · DOI
  87. Wilson RB (1963) A simplicial algorithm for concave programming. PhD thesis, Gradaute School of Business Administration, Harvard University
  88. Yamada S, Tanino T, Inuiguchi M (2000) Inner approximation method for a reverse convex programming problem. J Optim Theory Appl 107(2):355–389 · DOI
  89. Yu CNJ, Joachims T (2009) Learning structural SVMs with latent variables. In: Proceedings of the 26th annual international conference on machine learning, pp 1169–1176 · DOI
  90. Yuille AL, Rangarajan A (2003) The concave-convex procedure. Neural Comput 15(4):915–936 · DOI · Paper page
  91. Zangwill WI (1969) Nonlinear programming: a unified approach. Prentice-Hall Inc, Englewood Cliffs
  92. Zillober C (2001) Global convergence of a nonlinear programming method using convex optimization. Numer Algorithms 27(3):265–289 · DOI

Cited by

Sorted by citations

Metadata

Authors
Lipp, T., & Boyd, S.
Affiliations
Stanford University (US)
Corresponding author
  • Lipp, Thomas
  • Boyd, Stephen
Venue
Optimization and Engineering
Published
2015-11-05
Volume
17
Issue
2
Pages
263-287
ISSN
  • 1389-4420 (ISSN-L)
  • 1573-2924
OpenAlex
W2221524898
Cited by
744
References
2
Citations by year
2026: 34 · 2025: 84 · 2024: 79 · 2023: 85 · 2022: 91 · 2021: 115 · 2020: 90 · 2019: 53 · 2018: 58 · 2017: 38 · 2016: 16 · 2015: 1
FWCI
42.51
Type
journal article
Language
en
Open access
closed
Locations
Optimization and Engineering (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
Keywords
concave-convex procedure, difference of convex programming, local optima, traveling salesman problem, vector inequalities, local heuristics

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review