R. Rockafellar - Academia.edu (original) (raw)

Papers by R. Rockafellar

Nondifferentiable Optimization: Motivations and Applications, 1985

Control problems with fully convex Lagrangians and convex initial costs are considered. Generaliz... more Control problems with fully convex Lagrangians and convex initial costs are considered. Generalized conjugacy and envelope representation in terms of a dualizing kernel are employed to recover the initial cost from the value function at some fixed future time, leading to a generalization of the cancellation rule for inf-convolution. Such recovery is possible subject to persistence of trajectories of a generalized Hamiltonian system, associated with the Lagrangian. Global analysis of Hamiltonian trajectories is carried out, leading to conditions on the Hamiltonian, and the corresponding Lagrangian, guaranteeing persistence of the trajectories.

Mathematics of Operations Research, 2015

The paper is devoted to full stability of optimal solutions in general settings of finite-dimensi... more The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems, including those of conic and specifically semidefinite programming. Developing a new technique of variational analysis and generalized differentiation, we derive second-order characterizations of full stability, in both Lipschitzian and Hölderian settings, and establish their relationships with the conventional notions of strong regularity and strong stability for a large class of problems of constrained optimization with twice continuously differentiable data.

SIAM Journal on Optimization, 1996

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1989

SSRN Electronic Journal, 2011

Optimization problems in discrete time can be modeled more flexibly by extended linear- quadratic... more Optimization problems in discrete time can be modeled more flexibly by extended linear- quadratic programming than by traditional linear or quadratic programming, because penalties and other expressions that may substitute for constraints can readily be incorporated and dualized. At the same time, dynamics can be written with state vectors as in dynamic programming and optimal control. This suggests new primal-dual approaches to solving multistage problems. The special setting for such numerical methods is described. New results are presented on the calculation of gradients of the primal and dual objective functions and on the convergence eects of strict quadratic regularization.

Transactions of the American Mathematical Society, 1994

Surveys in Operations Research and Management Science, 2013

SIAM Journal on Control and Optimization, 2013

Proceedings of the American Mathematical Society, 1992

Let LSC ⁡ ( X ) \operatorname {LSC} (X) denote the extended real-valued lower semicontinuous func... more Let LSC ⁡ ( X ) \operatorname {LSC} (X) denote the extended real-valued lower semicontinuous functions on a separable metrizable space X X . We show that a sequence ⟨ f n ⟩ \left \langle {{f_n}} \right \rangle in LSC ⁡ ( X ) \operatorname {LSC} (X) is epi-convergent to f ∈ LSC ⁡ ( X ) f \in \operatorname {LSC} (X) if and only for each real α \alpha , the level set of height α \alpha of f f can be recovered as the Painlevé-Kuratowski limit of an appropriately chosen sequence of level sets of the f n {f_n} at heights α n {\alpha _n} approaching α \alpha . Assuming the continuum hypothesis, this result fails without separability. An analogous result holds for weakly lower semicontinuous functions defined on a separable Banach space with respect to Mosco epi-convergence.

Proceedings of the American Mathematical Society, 1965

Mathematics of Operations Research, 2008

A framework is set up in which linear regression, as a way of approximating a random variable by ... more A framework is set up in which linear regression, as a way of approximating a random variable by other random variables, can be carried out in a variety of ways, which, moreover, can be tuned to the needs of a particular model in finance, or operations research more broadly. Although the idea of adapting the form of regression to the circumstances at hand has already found advocates in promoting quantile regression as an alternative to classical least-squares approaches, it is carried here much farther than that. Axiomatic concepts of error measure, deviation measure, and risk measure are coordinated with certain “statistics” that likewise say something about a random variable. Problems of regression utilizing these concepts are analyzed and the character of their solutions is explored in a range of examples. Special attention is paid to parametric forms of regression which arise in connection with factor models. It is argued that when different aspects of risk enter an optimization...

Mathematics of Operations Research, 1976

The theory of the proximal point algorithm for maximal monotone operators is applied to three alg... more The theory of the proximal point algorithm for maximal monotone operators is applied to three algorithms for solving convex programs, one of which has not previously been formulated. Rate-of-convergence results for the “method of multipliers,” of the strong sort already known, are derived in a generalized form relevant also to problems beyond the compass of the standard second-order conditions for oplimality. The new algorithm, the “proximal method of multipliers,” is shown to have much the same convergence properties, but with some potential advantages.

Mathematical Programming, 2013

Mathematical Programming, 2006

Journal of Banking & Finance, 2006