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作者：Zhou, XY
摘要：Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns dynamic near-optimization, or near-optimal controls, for systems governed by deterministic ordinary differential equations, and uses dynamic programming to study the near-optimality. Since nonsmoothness is inherent in this subject, the viscosity solution approach is employed to investigate the problem. The dynamic programming equation is derived in terms of epsilon-superdifferen...
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作者：Lewis, AS
摘要：A spectral function of a Hermitian matrix X is a function which depends only on the eigenvalues of X, lambda(1)(X) greater than or equal to lambda(2)(X) greater than or equal to ... greater than or equal to lambda(n)(X), and hence may be written f(lambda(2)(X), lambda(2)(X),..., lambda(n)(X)) for some symmetric function f. Such functions appear in a wide variety of matrix optimization problems. We give a simple proof that this spectral function is differentiable at X if and only if the functio...
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作者：Monteiro, RDC; Pang, JS
作者单位：Johns Hopkins University
摘要：Using a unified theory of local homeomorphic maps, we establish some basic properties of a fundamental mapping associated with the family of path-following interior-point methods for solving a mixed nonlinear complementarity problem.
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作者：More, JJ
摘要：Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only require...
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作者：Goldfarb, D; Jin, ZY
摘要：This paper presents a modified version of Algorithm MCF proposed by Goldberg, Plotkin and Tardos for the generalized circulation problem. This new combinatorial algorithm has a worst-case complexity that is better than the complexities of the MCF and Fat-Path combinatorial algorithms of Goldberg, Plotkin, and Tardos (1991).
