Kanno,
Y.
, 2016, “
Global Optimization of Trusses With Constraints on Number of Different Cross-Sections: A Mixed-Integer Second-Order Cone Programming Approach,” Comput. Optim. Appl.,
63(1), pp. 203–236.

[CrossRef]
Boyd,
S.
,
Parikh,
N.
,
Chu,
E.
,
Peleato,
B.
, and
Eckstein,
J.
, 2010, “
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations Trends Mach. Learn.,
3(1), pp. 1–122.

[CrossRef]
Jung,
Y.
,
Kang,
N.
, and
Lee,
I.
, 2018, “
Modified Augmented Lagrangian Coordination and Alternating Direction Method of Multipliers With Parallelization in Non-Hierarchical Analytical Target Cascading,” Struct. Multidiscip. Optim.,
58(2), pp. 555–573.

Tosserams,
S.
,
Etman,
L. F. P.
,
Papalambros,
P. Y.
, and
Rooda,
J. E.
, 2006, “
An Augmented Lagrangian Relaxation for Analytical Target Cascading Using the Alternating Direction Method of Multipliers,” Struct. Multidiscip. Optim.,
31(3), pp. 176–189.

[CrossRef]
Tosserams,
S.
,
Etman,
L. F. P.
, and
Rooda,
J. E.
, 2007, “
An Augmented Lagrangian Decomposition Method for Quasi-Separable Problems in MDO,” Struct. Multidiscip. Optim.,
34(3), pp. 211–227.

[CrossRef]
Xu,
M.
,
Fadel,
G.
, and
Wiecek,
M. M.
, 2017, “
Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals,” ASME J. Mech. Des.,
139(3), p. 031401.

Ames,
B. P. W.
, and
Hong,
M.
, 2016, “
Alternating Direction Method of Multipliers for Penalized Zero-Variance Discriminant Analysis,” Comput. Optim. Appl.,
64(3), pp. 725–754.

[CrossRef]
Diamond,
S.
,
Takapoui,
R.
, and
Boyd,
S.
, 2018, “
A General System for Heuristic Minimization of Convex Functions Over Non-Convex Sets,” Optim. Methods Software,
33(1), pp. 165–193.

[CrossRef]
Takapoui,
R.
,
Moehle,
N.
,
Boyd,
S.
, and
Bemporad,
A.
, 2017, “
A Simple Effective Heuristic for Embedded Mixed-Integer Quadratic Programming,” Int. J. Control (epub).

Chartrand,
R.
, 2012, “
Nonconvex Splitting for Regularized Low-Rank + Sparse Decomposition,” IEEE Trans. Signal Process.,
60(11), pp. 5810–5819.

[CrossRef]
Chartrand,
R.
, and
Wohlberg,
B.
, 2013, “
A Nonconvex ADMM Algorithm for Group Sparsity With Sparse Groups,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada, May 26–31, pp. 6009–6013.

Kanamori,
T.
, and
Takeda,
A.
, 2014, “
Numerical Study of Learning Algorithms on Stiefel Manifold,” Comput. Manage. Sci.,
11(4), pp. 319–340.

[CrossRef]
Kanno,
Y.
, and
Fujita,
S.
, 2018, “
Alternating Direction Method of Multipliers for Truss Topology Optimization With Limited Number of Nodes: A Cardinality-Constrained Second-Order Cone Programming Approach,” Optim. Eng.,
19(2), pp. 327–358.

[CrossRef]
Kanno,
Y.
, and
Kitayama,
S.
, 2018, “
Alternating Direction Method of Multipliers as a Simple Effective Heuristic for Mixed-Integer Nonlinear Optimization,” Struct. Multidiscip. Optim.,
58(3), pp. 1291–1295.

M. F. Anjos
, and
J. B. Lasserre
, eds., 2012, Handbook on Semidefinite, Conic and Polynomial Optimization,
Springer,
New York.

Ben-Tal,
A.
, and
Nemirovski,
A.
, 2001, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications,
SIAM,
Philadelphia, PA.

Kanno,
Y.
, and
Yamada,
H.
, 2017, “
A Note on Truss Topology Optimization under Self-Weight Load: Mixed-Integer Second-Order Cone Programming Approach,” Struct. Multidiscip. Optim.,
56(1), pp. 221–226.

[CrossRef]
Kanno,
Y.
, 2016, “
Mixed-Integer Second-Order Cone Programming for Global Optimization of Compliance of Frame Structure With Discrete Design Variables,” Struct. Multidiscip. Optim.,
54(2), pp. 301–316.

[CrossRef]
Kanno,
Y.
, 2013, “
Damper Placement Optimization in a Shear Building Model With Discrete Design Variables: A Mixed-Integer Second-Order Cone Programming Approach,” Earthquake Eng. Struct. Dyn.,
42(11), pp. 1657–1676.

[CrossRef]
Kanno,
Y.
, and
Guo,
X.
, 2010, “
A Mixed Integer Programming for Robust Truss Topology Optimization With Stress Constraints,” Int. J. Numer. Methods Eng.,
83(13), pp. 1675–1699.

[CrossRef]
Mela,
K.
, 2014, “
Resolving Issues With Member Buckling in Truss Topology Optimization Using a Mixed Variable Approach,” Struct. Multidiscip. Optim.,
50(6), pp. 1037–1049.

[CrossRef]
Rasmussen,
M. H.
, and
Stolpe,
M.
, 2008, “
Global Optimization of Discrete Truss Topology Design Problems Using a Parallel Cut-and-Branch Method,” Comput. Struct.,
86(13–14), pp. 1527–1538.

[CrossRef]
Stolpe,
M.
, 2007, “
On the Reformulation of Topology Optimization Problems as Linear or Convex Quadratic Mixed 0-1 Programs,” Optim. Eng.,
8(2), pp. 163–192.

[CrossRef]
Hirota,
M.
, and
Kanno,
Y.
, 2015, “
Optimal Design of Periodic Frame Structures With Negative Thermal Expansion via Mixed Integer Programming,” Optim. Eng.,
16(4), pp. 767–809.

[CrossRef]
Kureta,
R.
, and
Kanno,
Y.
, 2014, “
A Mixed Integer Programming Approach to Designing Periodic Frame Structures With Negative Poisson's Ratio,” Optim. Eng.,
15(3), pp. 773–800.

[CrossRef]
Van Mellaert,
R.
,
Mela,
K.
,
Tiainen,
T.
,
Heinisuo,
M.
,
Lombaert,
G.
, and
Schevenels,
M.
, 2018, “
Mixed-Integer Linear Programming Approach for Global Discrete Sizing Optimization of Frame Structures,” Struct. Multidiscip. Optim.,
57(2), pp. 579–593.

[CrossRef]
Stolpe,
M.
, and
Stidsen,
T.
, 2007, “
A Hierarchical Method for Discrete Structural Topology Design Problems With Local Stress and Displacement Constraints,” Int. J. Numer. Methods Eng.,
69(5), pp. 1060–1084.

[CrossRef]
Stolpe,
M.
, and
Svanberg,
K.
, 2003, “
Modelling Topology Optimization Problems as Linear Mixed 0-1 Programs,” Int. J. Numer. Methods Eng.,
57(5), pp. 723–739.

[CrossRef]
Svanberg,
K.
, and
Werme,
M.
, 2007, “
Sequential Integer Programming Methods for Stress Constrained Topology Optimization,” Struct. Multidiscip. Optim.,
34(4), pp. 277–299.

[CrossRef]
Ehara,
S.
, and
Kanno,
Y.
, 2010, “
Topology Design of Tensegrity Structures via Mixed Integer Programming,” Int. J. Solids Struct.,
47(5), pp. 571–579.

[CrossRef]
Kanno,
Y.
, 2012, “
Topology Optimization of Tensegrity Structures Under Self-Weight Loads,” J. Oper. Res. Soc. Jpn.,
55(2), pp. 125–145.

[CrossRef]
Kanno,
Y.
, 2013, “
Topology Optimization of Tensegrity Structures Under Compliance Constraint: A Mixed Integer Linear Programming Approach,” Optim. Eng.,
14(1), pp. 61–96.

[CrossRef]
Kanno,
Y.
, 2013, “
Exploring New Tensegrity Structures via Mixed Integer Programming,” Struct. Multidiscip. Optim.,
48(1), pp. 95–114.

[CrossRef]
Pandian,
N. K. R.
, and
Ananthasuresh,
G. K.
, 2017, “
Synthesis of Tensegrity Structures of Desired Shape Using Constrained Minimization,” Struct. Multidiscip. Optim.,
56(6), pp. 1233–1245.

[CrossRef]
Pietroni,
N.
,
Tarini,
M.
,
Vaxman,
A.
,
Panozzo,
D.
, and
Cignoni,
P.
, 2017, “
Position-Based Tensegrity Design,” ACM Trans. Graph.,
36(6), p. 172.

[CrossRef]
Xu,
X.
,
Wang,
Y.
, and
Luo,
Y.
, 2016, “
General Approach for Topology-Finding of Tensegrity Structures,” ASCE J. Struct. Eng.,
142(10), p. 04016061.

[CrossRef]
Quan,
N.
, and
Kim,
H. M.
, 2016, “
A Mixed Integer Linear Programming Formulation for Unrestricted Wind Farm Layout Optimization,” ASME J. Mech. Des.,
138(6), p. 061404.

[CrossRef]
Turner,
S. D. O.
,
Romero,
D. A.
,
Zhang,
P. Y.
,
Amon,
C. H.
, and
Chan,
T. C. Y.
, 2014, “
A New Mathematical Programming Approach to Optimize Wind Farm Layouts,” Renewable Energy,
63, pp. 674–680.

[CrossRef]
Stolpe,
M.
, 2016, “
Truss Optimization With Discrete Design Variables: A Critical Review,” Struct. Multidiscip. Optim.,
53(2), pp. 349–374.

[CrossRef]
Demeulenaere,
B.
,
Aertbeliën,
E.
,
Verschuure,
M.
,
Swevers,
J.
, and
De Schutter,
J.
, 2006, “
Ultimate Limits for Counterweight Balancing of Crank-Rocker Four-Bar Linkages,” ASME J. Mech. Des.,
128(6), pp. 1272–1234.

[CrossRef]
Demeulenaere,
B.
,
Verschuure,
M.
,
Swevers,
J.
, and
De Schutter,
J.
, 2010, “
A General and Numerically Efficient Framework to Design Sector-Type and Cylindrical Counterweights for Balancing of Planar Linkages,” ASME J. Mech. Des.,
132(1), p. 011002.

[CrossRef]
Verschuure,
M.
,
Demeulenaere,
B.
,
Swevers,
J.
, and
Schutter,
J. D.
, 2008, “
Counterweight Balancing for Vibration Reduction of Elastically Mounted Machine Frames: A Second-Order Cone Programming Approach,” ASME J. Mech. Des.,
130(2), p. 022302.

[CrossRef]
Meng,
J.
,
Zhang,
D.
, and
Li,
Z.
, 2009, “
Accuracy Analysis of Parallel Manipulators With Joint Clearance,” ASME J. Mech. Des.,
131(1), p. 011013.

[CrossRef]
Asadpoure,
A.
,
Guest,
J. K.
, and
Valdevit,
L.
, 2015, “
Incorporating Fabrication Cost into Topology Optimization of Discrete Structures and Lattices,” Struct. Multidiscip. Optim.,
51(2), pp. 385–396.

[CrossRef]
Torii,
A. J.
,
Lopez,
R. H.
, and
F. Miguel,
L. F.
, 2016, “
Design Complexity Control in Truss Optimization,” Struct. Multidiscip. Optim.,
54(2), pp. 289–299.

[CrossRef]
Lavan,
O.
, and
Amir,
O.
, 2014, “
Simultaneous Topology and Sizing Optimization of Viscous Dampers in Seismic Retrofitting of 3D Irregular Frame Structures,” Earthquake Eng. Struct. Dyn.,
43(9), pp. 1325–1342.

[CrossRef]
Barbosa,
H. J. C.
,
Lemonge,
A. C. C.
, and
Borges,
C. C. H.
, 2008, “
A Genetic Algorithm Encoding for Cardinality Constraints and Automatic Variable Linking in Structural Optimization,” Eng. Struct.,
30(12), pp. 3708–3723.

[CrossRef]
Carvalho,
J. P. G.
,
Lemonge,
A. C. C.
,
Carvalho,
É. C. R.
,
Hallak,
P. H.
, and
Bernardino,
H. S.
, 2018, “
Truss Optimization With Multiple Frequency Constraints and Automatic Member Grouping,” Struct. Multidiscip. Optim.,
57(2), pp. 547–577.

[CrossRef]
Galante,
M.
, 1996, “
Genetic Algorithms as an Approach to Optimize Real-World Trusses,” Int. J. Numer. Methods Eng.,
39(3), pp. 361–382.

[CrossRef]
Shea,
K.
,
Cagan,
J.
, and
Fenves,
S. J.
, 1997, “
A Shape Annealing Approach to Optimal Truss Design With Dynamic Grouping of Members,” ASME J. Mech. Des.,
119(3), pp. 388–394.

[CrossRef]
Toğan,
V.
, and
Daloğlu,
A. T.
, 2006, “
Optimization of 3D Trusses With Adaptive Approach in Genetic Algorithms,” Eng. Struct.,
28(7), pp. 1019–1027.

[CrossRef]
Boyd,
S.
, and
Vandenberghe,
L.
, 2004, Convex Optimization,
Cambridge University Press,
Cambridge, UK.

Benson,
H. Y.
, and
Sa,
Ü.
, 2013, “
Ğlan: Mixed-Integer Second-Order Cone Programming: A Survey,” INFORMS Tutorials in Operations Research: Theory Driven by Influential Applications,
H. Topaloglu
, ed.,
INFORMS, Catonsville, pp. 13–36.

Kočvara,
M.
, 2017, “
Truss Topology Design by Linear Conic Optimization,” Advances and Trends in Optimization With Engineering Applications,
T. Terlaky
,
M. F. Anjos
, and
S. Ahmed
, eds.,
SIAM,
Philadelphia, PA, pp. 149–160.

Makrodimopoulos,
A.
,
Bhaskar,
A.
, and
Keane,
A. J.
, 2010, “
Second-Order Cone Programming Formulations for a Class of Problems in Structural Optimization,” Struct. Multidiscip. Optim.,
40(1–6), pp. 365–380.

[CrossRef]
Grant,
M.
, and
Boyd,
S.
, 2008, “
Graph Implementations for Nonsmooth Convex Programs,” Recent Advances in Learning and Control (a Tribute to M. Vidyasagar),
V. Blondel
,
S. Boyd
, and
H. Kimura
, eds.,
Springer-Verlag, London, pp. 95–110.

Grant,
M.
, and
Boyd,
S.
, 2018, “
CVX: Matlab Software for Disciplined Convex Programming, Ver. 2.1,” CVX Research Inc., San Mateo, CA, accessed Aug. 29, 2018

http://cvxr.com/cvx/
Tütüncü,
R. H.
,
Toh,
K. C.
, and
Todd,
M. J.
, 2003, “
Solving Semidefinite-Quadratic-Linear Programs Using SDPT3,” Math. Program.,
B95(2), pp. 189–217.

[CrossRef]
Guo,
X.
,
Bai,
W.
, and
Zhang,
W.
, 2008, “
Extreme Structural Response Analysis of Truss Structures Under Material Uncertainty Via Linear Mixed 0-1 Programming,” Int. J. Numer. Methods Eng.,
76(3), pp. 253–277.

[CrossRef]
Guo,
X.
,
Bai,
W.
,
Zhang,
W.
, and
Gao,
X.
, 2009, “
Confidence Structural Robust Design and Optimization Under Stiffness and Load Uncertainties,” Comput. Methods Appl. Mech. Eng.,
198(41–44), pp. 3378–3399.

[CrossRef]
Kanno,
Y.
, and
Takewaki,
I.
, 2006, “
Confidence Ellipsoids for Static Response of Trusses With Load and Structural Uncertainties,” Comput. Methods Appl. Mech. Eng.,
196(1–3), pp. 393–403.

[CrossRef]