Variational Analysis

Variational Analysis

[52] J. Royset and R. Wets. From data to assessments and decisions:

epi-spline technology, INFORMS Tutorials in Operations Research, 27-53,

November 2014 (San Francisco, INFORMS Meeting).

[51] J. Royset and R. Wets. Epi-splines and exponential epi-splines: pliable

approximation tools, Tech. Report U. of California, Davis, 2013 (submitted)

[50] J. Royset, N. Sukumar and R. Wets, Uncertainty quantification using exponential

epi-splines, Proceedings of the International Conference on Structural

Safety and Reliability, New York, NY, 2013

[49] R. Wets. An Optimization Primer. AMS Graduate Texts or Springer (in progress), 2012.

[48] A. Jofré and R. Wets. Variational convergence of bivariate functions: Motivating

applications. SIAM Journal on Optimization, ??, xxx-xxx, 2014,

[47] A. Jofé and R. Wets. Variational convergence of bivariate functions: Lopsided

convergence. Mathematical Programming, Ser. B, 116:275–295, 2009.

[46] N. Sukumar and R. Wets. Deriving the continuity of maximum-entropy basis functions

via variational analysis. SIAM Journal on Optimization, 18:914–925, 2008.

[45] W. Römisch and R. Wets. Stability of ε-approximate solutions to convex stochastic

programs. SIAM Journal on Optimization, 18:961–979, 2007.

[44] J.-B. Hiriart-Urruty, C. Lemaréchal, B. Mordukhovich, J. Sun, and R. Wets, editors.

Variational Analysis, Optimization and Applications. SIAM Mathematical Programming

Society, 2006.

[43] R. Wets. Foreword: Variational Analysis, Optimization and Applications. Mathematical

Programming, Ser. B, 104:203–204, 2006.

[42] R. Wets. Lipschitz continuity of inf-projections. Computational Optimization and

Applications, 25:269–282, 2003.

[41] R.T. Rockafellar and R. Wets. Variational Analysis,

volume 317 of Grundlehren der Mathematischen Wissenschafte.

Springer, 1998 (3rd printing 2009). --- Preface

Errata - 1st Printing (1998), 2nd Printing (2004), 3rd Printing (2009)

[40] A. Bagh and R. Wets. Convergence of set-valued mappings: Equi-outer

semicontinuity. Set-Valued Analysis, 4:333–360, 1996.

[39] Y. Ermoliev, V. I. Norkin, and R. Wets. The minimization of discontinuous functions:

mollifier subgradients. SIAM J. on Control and Optimization, 33:149–167, 1995.

[38] Z. Artstein and R. Wets. Stability results for stochastic programs and sensors, allowing

for discontinuous objective functions. SIAM J. on Optimization, 4:537–550, 1995.

[37] H. Attouch and R. Wets. Quantitative stability of variational systems: II. A framework

for nonlinear conditioning. SIAM J. on Optimization, 3:359–381, 1993.

[36] H. Attouch and R. Wets. Quantitative stability of variational systems: III ε-approximate

solutions. Mathematical Programming, 61:197–214, 1993.

[35] R. Lucchetti, A. Torre, and R. Wets. A topology for the solid subsets of a topological

space. Canadian Mathematical Bulletin, 36:197–208, 1993.

[34] R.T. Rockafellar and R. Wets. Cosmic convergence. In A. Ioffe, M. Marcus and S.

Reich, editors, Optimization and Nonlinear Analysis, pages 249–272. Pitman Research

Notes in Mathematics Series 244, Longman House, 1992.

[33] G. Beer, R.T. Rockafellar, and R. Wets. A characterization of epi-convergence in

terms of convergence of level sets. Proceedings of the American Mathematical Society,

116:753–761, 1992.

[32] H. Attouch and R. Wets. Quantitative stability of variational systems: I. The

epigraphical distance. Transactions of the American Mathematical Society,

328:695–729, 1991.

[31] H. Attouch, R. Lucchetti, and R. Wets. The topology of the ρ-Hausdorff distance.

Annali di Matematica pura ed applicata, CLX:303–320, 1991.

[30] H. Attouch and R. Wets. Epigraphical analysis. In H. Attouch, J.-P. Aubin, F. Clarke,

and I. Ekeland, editors, Analyse Non Linéaire, pages 73–100. Gauthier-Villars, 1989.

[29] J.-P. Aubin and R. Wets. Stable approximations of set-valued maps.

Annales de l’Institut Henri Poincaré, 5:519–535, 1988.

[28] H. Attouch, D. Azé, and R. Wets. Convergence of convex-concave saddle functions:

continuity properties of the Legendre-Fenchel transform with applications to convex

programming and mechanics. Annales de l’Institut H. Poincaré: Analyse Nonlinéaire,

5:537–572, 1988.

[27] H. Attouch and R. Wets. Another isometry for the Legendre-Fenchel transform.

J. Mathematical Analysis and Applications, 131:404–411, 1988.

[26] S.D. Flåm and R. Wets. Existence results and finite horizon approximates for infinite

horizon optimization problems. Econometrica, 55:1187–1209, 1987.

[25] H. Attouch, D. Azé, and R. Wets. On the continuity properties of the partial

Legendre-Fenchel transform: convergence of sequences of augmented Lagrangian

functions, Moreau-Ypsida approximates and subdifferential operators

In J.-B. Hiriart-Urruty, editor, Fermat-Days 85: Mathematics for Optimization,

pages 1–42. North Holland, 1986.

[24] H. Attouch and R. Wets. Isometries for the Legendre-Fenchel transform

Transactions of the American Mathematical Society, 296:33–60, 1986.

[23] R. Wets. Finite time approximates to infinite horizon problems. In K. Lommatsch,

editor, Proceedings of the Optimization Conference: Seelin 1984, pages 240–243.

Humboldt University Press, 1984.

[22] R.T. Rockafellar and R. Wets. Variational systems, an introduction. In G. Salinetti,

editor, Multifunctions and Integrands: Stochastic Analysis, Approximation and Optimization,

pages 1–54. Springer Lecture Notes in Mathematics 1091, 1984.

[21] H. Attouch and R. Wets. Convergence des points min/sup et de points fixes.

Comptes Rendus de l’Académie des Sciences de Paris, 296:657–660, 1983.

[20] S. Dolecki, G. Salinetti, and R. Wets. Convergence of functions: equi-semicontinuity.

Transactions of the American Mathematical Society, 276:409–429, 1983.

[19] R. Wets. A formula for the level sets of epi-limits and some applications. In

J.P. Cecconi and T. Zolezzi, editors, Mathematical Theories of Optimization,

pages 256–268. Springer, 1983.

[18] H. Attouch and R. Wets. A convergence for bivariate functions aimed at the

convergence of saddle values. In J.P. Cecconi and T. Zolezzi, editors, Mathematical

Theories of Optimizations, pages 1–42. Springer, 1983.

[17] H. Attouch and R. Wets. A convergence theory for saddle functions.

Transactions of the American Mathematical Society, 280:1–41, 1983.

[16] R. Wets. On a compactness theorem for epi-convergent sequences of functions.

In R. Cottle, M. Kelmason, and B. Korte, editors, Mathematical Programming,

pages 347–355. North Holland, 1983.

[15] R. Wets. Convergence of sequences of closed functions. In A. Fiacco, editor,

Proceedings Symposium on Mathematical Programming with Data Perturbations,

pages 16–27. Marcel Dekker, 1982.

[14] G. Salinetti and R. Wets. On the convergence of closed-valued measurable

multifunctions. Transactions of the American Mathematical Society, 266:275–289, 1981.

[13] H. Attouch and R. Wets. Approximation and convergence in nonlinear optimization.

In O. Mangasarian, R. Meyer, and S. Robinson, editors, Nonlinear Programming 4,

pages 367–394. Academic Press, 1981.

[12] R. Wets. Convergence of convex functions, variational inequalities and convex

optimization problems. In R. Cottle, F. Giannessi, and J.L. Lions, editors,

Variational Inequalities and Complementarity Problems, pages 405–419. Wiley, 1980.

[11] R. Wets. Marginal valued functions. University of Kentucky, Manuscript, 1979.

[10] G. Salinetti and R. Wets. On the convergence of sequences of convex sets in finite

dimensions. SIAM Review, 21:16–33, 1979.

[ 9] G. Salinetti and R. Wets. Convergence of sequences of closed sets. Topology

Proceedings, 4:149–158, 1979.

[ 8] G. Salinetti and R. Wets. On the relation between two types of convergence for

convex functions.J. Mathematical Analysis and Applications, 60:211–226, 1977.

[ 7] R. Wets. Grundlage Konvexer Optimierung. Springer, 1976.

[ 6] R. Wets. On inf-compact mathematical programs. In Fifth Conference on Optimization

Techniques, Part I., volume 5 of Lecture Notes in Computer Science, pages 426–436.

Springer, 1974.

[ 5] R. Wets. On the measurability of the subgradients of a parametrized family of convex

functions. Operations Research Verfahren, 10:232–239, 1971.

[ 4] R. Wets. Necessary and sufficient conditions for optimality: A geometric approach.

Operations Research Verfahren, 8:305–311, 1970.

[ 3] D. Walkup and R. Wets. Some practical regularity conditions for nonlinear programs.

SIAM J. Control, 7:430–436, 1969.

[ 2] R. Van Slyke and R. Wets. A duality theory for abstract mathemtical programs with

applications to optimal control theory. J. Mathematical Analysis and Applications,

22:679–706, 1968.

[ 1] D. Walkup and R. Wets. Continuity of some convex-cone-valued mappingsl.

Proceedings of the American Mathematical Society, 18:229–235, 1967.