-
1
-
-
45849133389
-
On augmented Lagrangian methods with general lower-level constraints
-
R. Andreani, E.G. Birgin, J.M. Martínez, and M.L. Schuverdt, On augmented Lagrangian methods with general lower-level constraints, SIAM J. Optim. 18 (2007), pp. 1286-1309.
-
(2007)
SIAM J. Optim
, vol.18
, pp. 1286-1309
-
-
Andreani, R.1
Birgin, E.G.2
Martínez, J.M.3
Schuverdt, M.L.4
-
2
-
-
34347264176
-
Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
-
_, Augmented Lagrangian methods under the constant positive linear dependence constraint qualification, Math. Program. 111 (2008), pp. 5-32.
-
(2008)
Math. Program
, vol.111
, pp. 5-32
-
-
Andreani, R.1
Birgin, E.G.2
Martínez, J.M.3
Schuverdt, M.L.4
-
3
-
-
0023410362
-
Recursive quadratic programming methods based on the augmented Lagmngian function
-
M.C. Bartholomew-Biggs, Recursive quadratic programming methods based on the augmented Lagmngian function, Math. Program. Study 31 (1987), pp. 21-41.
-
(1987)
Math. Program. Study
, vol.31
, pp. 21-41
-
-
Bartholomew-Biggs, M.C.1
-
5
-
-
18844418678
-
Numerical comparison of augmented Lagrangian algorithms for nonconvexproblems
-
E.G. Birgin, R. A. Castillo, and J.M. Martínez, Numerical comparison of augmented Lagrangian algorithms for nonconvexproblems, Comput. Optim. Appl. 31 (2005), pp. 31-55.
-
(2005)
Comput. Optim. Appl
, vol.31
, pp. 31-55
-
-
Birgin, E.G.1
Castillo, R.A.2
Martínez, J.M.3
-
6
-
-
77249083301
-
-
Tech. Rep, Department of Computer Science IME-USP, University of São Paulo, Brazil, Available in Optimization Online
-
E.G. Birgin, CA. Floudas, and J.M. Martinez, Global minimization using an augmented Lagrangian method with variable lower-level constraints, Tech. Rep., Department of Computer Science IME-USP, University of São Paulo, Brazil, 2006. Available in Optimization Online.
-
(2006)
Global minimization using an augmented Lagrangian method with variable lower-level constraints
-
-
Birgin, E.G.1
Floudas, C.A.2
Martinez, J.M.3
-
7
-
-
34848874471
-
On the absence of duality gap for Lagrange-type functions
-
R.S. Burachik and A.M. Rubinov, On the absence of duality gap for Lagrange-type functions, J. Industrial Manage. Optim. 1 (2005), pp. 33-38.
-
(2005)
J. Industrial Manage. Optim
, vol.1
, pp. 33-38
-
-
Burachik, R.S.1
Rubinov, A.M.2
-
8
-
-
35148834472
-
Abstract convexity and augmented Lagrangians
-
_, Abstract convexity and augmented Lagrangians, SIAM J. Optim. 18 (2007), pp. 413-436.
-
(2007)
SIAM J. Optim
, vol.18
, pp. 413-436
-
-
Burachik, R.S.1
Rubinov, A.M.2
-
9
-
-
34249771074
-
On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds
-
T.F. Coleman and Y. Li, On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds, Math. Program. 67 (1994), pp. 189-224.
-
(1994)
Math. Program
, vol.67
, pp. 189-224
-
-
Coleman, T.F.1
Li, Y.2
-
10
-
-
0030303844
-
An interior trust region approach for nonlinear minimization subject to bounds
-
_, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim. 6 (1996), pp. 418-445.
-
(1996)
SIAM J. Optim
, vol.6
, pp. 418-445
-
-
Coleman, T.F.1
Li, Y.2
-
11
-
-
0036013031
-
An augmented Lagrangian function with improved exactness properties
-
G. Di Pillo and S. Lucidi, An augmented Lagrangian function with improved exactness properties, SIAM J. Optim. 12 (2001), pp. 376-406.
-
(2001)
SIAM J. Optim
, vol.12
, pp. 376-406
-
-
Di Pillo, G.1
Lucidi, S.2
-
12
-
-
0026136104
-
A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds
-
A.R. Conn, N.I.M. Gould, and P.L. Toint, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal. 28 (1991), pp. 545-572.
-
(1991)
SIAM J. Numer. Anal
, vol.28
, pp. 545-572
-
-
Conn, A.R.1
Gould, N.I.M.2
Toint, P.L.3
-
13
-
-
0030303858
-
Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints
-
A.R. Conn, N.I.M. Gould, A. Sartenaer, and P.L. Toint, Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints, SIAM J. Optim. 6 (1996), pp. 674-703.
-
(1996)
SIAM J. Optim
, vol.6
, pp. 674-703
-
-
Conn, A.R.1
Gould, N.I.M.2
Sartenaer, A.3
Toint, P.L.4
-
14
-
-
0027701845
-
Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints
-
L. Contesse-Becker, Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints, J. Optim. Theory Appl. 79 (1993), pp. 273-310.
-
(1993)
J. Optim. Theory Appl
, vol.79
, pp. 273-310
-
-
Contesse-Becker, L.1
-
15
-
-
0003817849
-
-
Kluwer Academic Publishers, Dordrecht
-
C.A. Floudas, P.M. Pardalos, C.S. Adjiman, W.R. Esposito, Z.H. Gumus, S.T. Harding, J.L. Klepeis, C.A. Meyer, and C.A. Schweiger, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, Dordrecht, 1999.
-
(1999)
Handbook of Test Problems in Local and Global Optimization
-
-
Floudas, C.A.1
Pardalos, P.M.2
Adjiman, C.S.3
Esposito, W.R.4
Gumus, Z.H.5
Harding, S.T.6
Klepeis, J.L.7
Meyer, C.A.8
Schweiger, C.A.9
-
16
-
-
31744440498
-
A primal-dual nonlinear rescaling method with dynamic scaling parameter update
-
I. Griva and R. Polyak, A primal-dual nonlinear rescaling method with dynamic scaling parameter update, Math. Program. 106 (2006), pp. 237-259.
-
(2006)
Math. Program
, vol.106
, pp. 237-259
-
-
Griva, I.1
Polyak, R.2
-
17
-
-
0023434929
-
Dual techniques for constrained optimization
-
W.W. Hager, Dual techniques for constrained optimization, J. Optim. Theory Appl. 55 (1987), pp. 37-71.
-
(1987)
J. Optim. Theory Appl
, vol.55
, pp. 37-71
-
-
Hager, W.W.1
-
18
-
-
0016535543
-
Iterative determination of parameters for an exact penalty function
-
J.K. Hartman, Iterative determination of parameters for an exact penalty function, J. Optim. Theory Appl. 16 (1975), pp. 49-66.
-
(1975)
J. Optim. Theory Appl
, vol.16
, pp. 49-66
-
-
Hartman, J.K.1
-
19
-
-
0014604308
-
Multiplier and gradient methods
-
M.R. Hestenes, Multiplier and gradient methods, J. Optim. Theory Appl. 4 (1969), pp. 303-320.
-
(1969)
J. Optim. Theory Appl
, vol.4
, pp. 303-320
-
-
Hestenes, M.R.1
-
20
-
-
0141740372
-
A unified augmented Lagrangian approach to duality and exact penalization
-
X.X. Huang and X.Q. Yang, A unified augmented Lagrangian approach to duality and exact penalization, Math. Oper. Res. 28 (2003), pp. 524-532.
-
(2003)
Math. Oper. Res
, vol.28
, pp. 524-532
-
-
Huang, X.X.1
Yang, X.Q.2
-
21
-
-
0030538897
-
On the twice differentiable cubic augmented Lagrangian
-
K.C. Kiwiel, On the twice differentiable cubic augmented Lagrangian, J. Optim. Theory Appl. 88 (1996), pp. 233-236.
-
(1996)
J. Optim. Theory Appl
, vol.88
, pp. 233-236
-
-
Kiwiel, K.C.1
-
23
-
-
0016922324
-
Combined primal-dual and penalty methods for convex programming
-
_, Combined primal-dual and penalty methods for convex programming, SIAM J. Control Optim. 14 (1976), pp. 268-294.
-
(1976)
SIAM J. Control Optim
, vol.14
, pp. 268-294
-
-
Kort, B.W.1
Bertsekas, D.P.2
-
24
-
-
0036436111
-
A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds
-
R.M. Lewis and V. Torczon, A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds, SIAM J. Optim. 12 (2002), pp. 1075- 1089.
-
(2002)
SIAM J. Optim
, vol.12
, pp. 1075-1089
-
-
Lewis, R.M.1
Torczon, V.2
-
25
-
-
21844506739
-
Zero duality gap for a class of nonconvex optimization problems
-
D. Li, Zero duality gap for a class of nonconvex optimization problems, J. Optim. Theory Appl. 85 (1995), pp. 309-324.
-
(1995)
J. Optim. Theory Appl
, vol.85
, pp. 309-324
-
-
Li, D.1
-
26
-
-
0034349450
-
Local convexification of the Lagrangian function in nonconvex optimization
-
D. Li and X.L. Sun, Local convexification of the Lagrangian function in nonconvex optimization, J. Optim. Theory Appl. 104 (2000), pp. 109-120.
-
(2000)
J. Optim. Theory Appl
, vol.104
, pp. 109-120
-
-
Li, D.1
Sun, X.L.2
-
27
-
-
0035423108
-
Convexification and existence of a saddle point in a pth-power reformulation for nonconvex constrained optimization
-
_, Convexification and existence of a saddle point in a pth-power reformulation for nonconvex constrained optimization, Nonlinear Anal. 47 (2001), pp. 5611-5622.
-
(2001)
Nonlinear Anal
, vol.47
, pp. 5611-5622
-
-
Li, D.1
Sun, X.L.2
-
28
-
-
0035446193
-
Existence of a saddle point in nonconvex constrained optimization
-
_, Existence of a saddle point in nonconvex constrained optimization, J. Global Optim. 21 (2001), pp. 39-50.
-
(2001)
J. Global Optim
, vol.21
, pp. 39-50
-
-
Li, D.1
Sun, X.L.2
-
29
-
-
52149102318
-
On the convergence of augmented Lagrangian methods for constrained global optimization
-
H.Z. Luo, X.L. Sun, and D. Li, On the convergence of augmented Lagrangian methods for constrained global optimization, SIAMJ. Optim. 18 (2007), pp. 1209-1230.
-
(2007)
SIAMJ. Optim
, vol.18
, pp. 1209-1230
-
-
Luo, H.Z.1
Sun, X.L.2
Li, D.3
-
30
-
-
0016533841
-
Unconstrained Lagrangians in nonlinear programming
-
O.L. Mangasarian, Unconstrained Lagrangians in nonlinear programming, SIAM J. Control Optim. 13 (1975), pp. 772-791.
-
(1975)
SIAM J. Control Optim
, vol.13
, pp. 772-791
-
-
Mangasarian, O.L.1
-
31
-
-
0018455554
-
On the convergence rate of a penalty function method of exponential type
-
V.H. Nguyen and J.J. Strodiot, On the convergence rate of a penalty function method of exponential type, J. Optim. Theory Appl. 27 (1979), pp. 495-508.
-
(1979)
J. Optim. Theory Appl
, vol.27
, pp. 495-508
-
-
Nguyen, V.H.1
Strodiot, J.J.2
-
32
-
-
34249830808
-
Modified barrier functions: Theory and methods
-
R. Polyak, Modified barrier functions: Theory and methods, Math. Program. 54 (1992), pp. 177-222.
-
(1992)
Math. Program
, vol.54
, pp. 177-222
-
-
Polyak, R.1
-
33
-
-
4043111445
-
Nonlinear rescaling vs. smoothing technique in convex optimization
-
_, Nonlinear rescaling vs. smoothing technique in convex optimization, Math. Program. 92(2002), pp. 197-235.
-
(2002)
Math. Program
, vol.92
, pp. 197-235
-
-
Polyak, R.1
-
34
-
-
0039922714
-
A globally convergent, implementable multiplier method with automatic penalty limitation
-
E. Polak and A.L. Tits, A globally convergent, implementable multiplier method with automatic penalty limitation, Appl. Math. Optim. 6 (1980), pp. 335-360.
-
(1980)
Appl. Math. Optim
, vol.6
, pp. 335-360
-
-
Polak, E.1
Tits, A.L.2
-
35
-
-
0346681529
-
-
R. Fletcher, ed, Academic Press, New York
-
M.J.D. Powell, A method for nonlinear constraints in minimization problems, Optimization, R. Fletcher, ed., Academic Press, New York, 1969, pp. 283-298.
-
(1969)
A method for nonlinear constraints in minimization problems, Optimization
, pp. 283-298
-
-
Powell, M.J.D.1
-
36
-
-
34250427726
-
The multiplier method of Hestenes and Powell applied to convex programming
-
R.T. Rockafellar, The multiplier method of Hestenes and Powell applied to convex programming, J. Optim. Theory Appl. 12 (1973), pp. 555-562.
-
(1973)
J. Optim. Theory Appl
, vol.12
, pp. 555-562
-
-
Rockafellar, R.T.1
-
37
-
-
0016059769
-
Augmented Lagrange multiplier functions and duality in nonconvex programming
-
_, Augmented Lagrange multiplier functions and duality in nonconvex programming, SIAM J. Control Optim. 12 (1974), pp. 268-285.
-
(1974)
SIAM J. Control Optim
, vol.12
, pp. 268-285
-
-
Rockafellar, R.T.1
-
38
-
-
0016950796
-
Augmented Lagrangians and applications of the proximal point algorithm in convex programming
-
_, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res. 1 (1976), pp. 97-116.
-
(1976)
Math. Oper. Res
, vol.1
, pp. 97-116
-
-
Rockafellar, R.T.1
-
39
-
-
0027606675
-
Lagrange multipliers and optimality
-
_, Lagrange multipliers and optimality, SIAM Rev. 35 (1993), pp. 183-238.
-
(1993)
SIAM Rev
, vol.35
, pp. 183-238
-
-
Rockafellar, R.T.1
-
42
-
-
0033261453
-
Decreasing functions with applications to penalization
-
A.M. Rubinov, B.M. Glover, and X.Q. Yang, Decreasing functions with applications to penalization, SIAM J. Optim. 10 (1999), pp. 289-313.
-
(1999)
SIAM J. Optim
, vol.10
, pp. 289-313
-
-
Rubinov, A.M.1
Glover, B.M.2
Yang, X.Q.3
-
43
-
-
0000606438
-
Modified Lagrangian and penalty functions in continuous optimization
-
_, Modified Lagrangian and penalty functions in continuous optimization, Optimization 46 (1999), pp. 327-351.
-
(1999)
Optimization
, vol.46
, pp. 327-351
-
-
Rubinov, A.M.1
Glover, B.M.2
Yang, X.Q.3
-
44
-
-
0036874360
-
The zero duality gap property and lower semi- continuity of the perturbation function
-
A.M. Rubinov, X.X. Huang, and X.Q. Yang, The zero duality gap property and lower semi- continuity of the perturbation function, Math. Oper. Res. 27 (2002), pp. 775-791.
-
(2002)
Math. Oper. Res
, vol.27
, pp. 775-791
-
-
Rubinov, A.M.1
Huang, X.X.2
Yang, X.Q.3
-
45
-
-
27844523996
-
On saddle points of augmented Lagrangians for constrained nonconvex optimization
-
X.L. Sun, D. Li, and K.I.M. McKinnon, On saddle points of augmented Lagrangians for constrained nonconvex optimization, SIAM J. Optim. 15 (2005), pp. 1128-1146.
-
(2005)
SIAM J. Optim
, vol.15
, pp. 1128-1146
-
-
Sun, X.L.1
Li, D.2
McKinnon, K.I.M.3
-
46
-
-
0027607344
-
On the convergence of the exponential multiplier method for convex programming
-
P. Tseng and D.P. Bertsekas, On the convergence of the exponential multiplier method for convex programming, Math. Program. 60 (1993), pp. 1-19.
-
(1993)
Math. Program
, vol.60
, pp. 1-19
-
-
Tseng, P.1
Bertsekas, D.P.2
-
47
-
-
0031536482
-
Local saddle points and convexification for nonconvex optimization problems
-
Z.K. Xu, Local saddle points and convexification for nonconvex optimization problems, J. Optim. Theory Appl. 94 (1997), pp. 739-746.
-
(1997)
J. Optim. Theory Appl
, vol.94
, pp. 739-746
-
-
Xu, Z.K.1
-
48
-
-
0020136870
-
A globally convergent constrained quasi-Newton method with an augmented Lagrangian type penalty function
-
H. Yamashita, A globally convergent constrained quasi-Newton method with an augmented Lagrangian type penalty function, Math. Program. 23 (1982), pp. 75-86.
-
(1982)
Math. Program
, vol.23
, pp. 75-86
-
-
Yamashita, H.1
-
49
-
-
0035621414
-
A nonlinear Lagrangian approach to constrained optimization problems
-
X.Q. Yang and X.X. Huang, A nonlinear Lagrangian approach to constrained optimization problems, SIAM J. Optim. 11 (2001), pp. 1119-1144.
-
(2001)
SIAM J. Optim
, vol.11
, pp. 1119-1144
-
-
Yang, X.Q.1
Huang, X.X.2
|