[1]

K.J. Arrow and L. Hurwicz, “Decentralization and computation in resource allocation”, in: R.W. Pfouts, ed.,*Essays in economics and econometrics*, University of North Carolina Press, Chapel Hill, N.C.; also in K.J. Arrow and L. Hurwicz, eds.,*Studies in resource allocation processes* (Cambridge University Press, 1977).

[2]

D.P. Bertsekas, “Convexification procedures and decomposition methods for nonconvex optimization problems”,*Journal of Optimization Theory and Applications* 29 (1979), 169–197.

[3]

G. Cohen, “Optimization by decomposition and coordination: A unified approach”, IEEE Transactions on Automatic Control, Vol. AC-23 (1978) 222–232.

[4]

G. Cohen, “Auxiliary problem principle and decomposition of optimization problems”,*Journal of Optimization Theory and Applications* 32 (1980) 277–305.

[5]

G.B. Dantzig and P. Wolfe, “Decomposition principle for linear programs”,*Operations Research* 8 (1960) 101–111.

[6]

G.B. Dantzig,*Linear programming and extensions* (Princeton University Press, Princeton, NJ, 1963).

[7]

I. Ekeland and R. Temam, Convex analysis and variational problems (North-Holland, 1976).

[8]

H. Everett, “Generalized Lagrange multiplier method for solving problems of optimum allocation of resources”,*Operations Research* 11 (1963) 399–417.

[9]

A.V. Fiacco, “Sensitivity analysis for nonlinear programming using penalty methods”,*Mathematical Programming* 10 (1976) 287–311.

[10]

W. Findeisen, F.N. Bailey, M. Brdyś, K. Malinowski, P. Tatjewski and A. Woźniak,*Control and coordination in hierarchical systems* (John Wiley & Sons, 1980).

[11]

M. Fortin and R. Glowinski, “On decomposition-coordination methods using an augmented Lagrangian”, in: M. Fortin and R. Glowinski, eds.,*Augmented Lagrangian methods: Applications to the numerical solution of boundary-value problems, Studies in Mathematics and its Applications* 15 (North-Holland, 1983).

[12]

M. Frank and P. Wolfe, “An algorithm for quadratic programming”,*Naval Research Logistics Quarterly* 3 (1956) 95–110.

[13]

D. Gabay and B. Mercier, “A dual algorithm for the solution of nonlinear variational problems via finite element approximation”,*Computers and Mathematics with Applications* 2 (1976) 17–40.

[14]

D. Gabay, “Applications of the method of multipliers to variational inequalities”, in: M. Fortin and R. Glowinski, eds.,*Augmented Lagrangian methods: Applications to the numerical solution of boundary-value problems* (North-Holland, Amsterdam, 1983).

[15]

A.M. Geoffrion, “Primal resource-directive approaches for optimizing nonlinear decomposable systems”,*Operations Research* 18 (1970) 375–403.

[16]

A. Geoffrion, “Large-scale linear and nonlinear programming”, in: D.A. Wismer, ed.,*Optimization methods for large-scale systems with applications* (McGraw-Hill, New York, 1971).

[17]

M.R. Hestenes, “Multiplier and gradient methods”,*Journal of Optimization Theory and Applications* (1969) 303–320.

[18]

L.S. Lasdon,*Optimization theory for large systems* (Macmillan, Toronto 1970).

[19]

L.S. Lasdon, “Decomposition in resource allocation”, in: D.M. Himmelblau, ed.,*Decomposition of large-scale problems* (North-Holland, 1973) 207–231.

[20]

F.J.R. Luque, “Asymptotic convergence analysis of the proximal point algorithm”,*SIAM Journal of Control and Optimization* 22 (1984) 277–293.

[21]

B. Martinet, “Determination approchée d'un point fixe d'une application pseudo-contractante. Cas de l'application prox”,*Comptes Rendus des Séances de l'Académie des Sciences*, Série A 274 (1972) 163–165.

[22]

G.J. Minty, “Monotone (nonlinear) operators in Hilbert space”,*Duke Mathematical Journal* 29 (1962) 341–346.

[23]

M.J.D. Powell, “A method for nonlinear constraints in minimization problems”, in: R. Fletcher, ed.,*Optimization* (Academic Press, NY, 1969) 283–298.

[24]

S.M. Robinson, “Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming problems”,*Mathematical Programming* 7 (1974) 1–16.

[25]

R.T. Rockafellar, “On the maximal monotonicity of subdifferential mappings”,*Pacific Journal of Mathematics* 33 (1970) 209–216.

[26]

R.T. Rockafellar,*Convex analysis* (Princeton University Press, Princeton, N.J. 1970).

[27]

R.T. Rockafellar, “The multiplier method of Hestenes and Powell applied to convex programming”,*Journal of Optimization Theory and Applications* 12 (1973) 555–562.

[28]

R.T. Rockafellar, “Augmented Lagrangians and applications of the proximal point algorithm in convex programming”,*Mathematics of Operations Research* 1 (1976) 97–116.

[29]

R.T. Rockafellar, “Monotone operators and the proximal point algorithm”,*SIAM Journal on Control and Optimization* 14 (1976) 877–898.

[30]

R.T. Rockafellar, “Monotone operators and augmented Lagrangian methods in nonlinear programming”, in: O.L. Mangasarian et al., eds.,*Nonlinear Programming ·3* (Academic Press, NY, 1978) 21–25.

[31]

R.T. Rockafellar, “Solving a nonlinear program by way of a dual problem”,*Symposia Mathematica* 19 (1976) 135–160.

[32]

J.E. Spingarn, “Fixed and variable constraints in sensitivity analysis”, SIAM Journal on Control and Optimization 18 (1980) 297–310.

[33]

J.E. Spingarn, “A proximal algorithm for decomposable convex programming”, summary abstract of this paper in Abstracts of the American Mathematical Society 6, October 1982.

[34]

J.E. Spingarn, “Partial inverse of a monotone operator”,*Applied Mathematics and Optimization* 10 (1983) 247–265.

[35]

J.E. Spingarn, “A primal-dual projection method for solving systems of linear inequalities”,*Linear Algebra and its Applications* 65 (1985) 45–62.

[36]

J.E. Spingarn, “A projection method for least square solutions to overdetermined systems of linear inequalities”, to appear.

[37]

G. Stephanopoulos and W. Westerberg, “The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization”,*Journal of Optimization Theory and Applications* 15 (1975) 285–309.

[38]

H. Uzawa, “Iterative methods for concave programming”, in: K. Arrow, L. Hurwicz, and H. Uzawa, eds.,*Studies in Linear and Nonlinear Programming* (Stanford University Press, Stanford, Ca, 1958).

[39]

N. Watanabe, Y. Nishimura and M. Matsubara, “Decomposition in large system optimization using the method of multipliers”,*Journal of Optimization Theory and Applications* 25 (1978) 181–193.