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Management Science, 1970
There is a dual program linked with every nonlinear program. The dual objective function is called the Lagrangian; it is defined in terms of the original problem. This note presents a characterization of the Lagrangian subgradients under general conditions. The theorem follows from a result of Danskin [1] that can be used (see [2]) to characterize the
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There is a dual program linked with every nonlinear program. The dual objective function is called the Lagrangian; it is defined in terms of the original problem. This note presents a characterization of the Lagrangian subgradients under general conditions. The theorem follows from a result of Danskin [1] that can be used (see [2]) to characterize the
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The Proximal Subgradient and Constancy
Canadian Mathematical Bulletin, 1993AbstractIf f is a lower semicontinuous function mapping a connected open subset of ℝn to (—∞, ∞], and if the proximal subgradient of f reduces to zero wherever it exists, then f is constant.
Clarke, F. H., Redheffer, R. M.
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A reduced subgradient algorithm
1987The authors describe an iterative method for the approximate solution of nondifferentiable convex programming problems. The problems incorporate linear equality and inequality constraints \((Ax=b\), \(x\geq 0)\); the method combines Wolfe's well-known reduced gradient algorithm with the bundle method of nonsmooth optimization.
Bihain, André +2 more
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A note on the existence of subgradients
Mathematical Programming, 1982We describe an apparently novel way of constructing the subgradient of a convex function defined on a finite dimensional vector space.
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Subgradient and ε-Subgradient Methods
1998Let us consider a convex programming problem (CPP): $$find{f^*} = \inf {f_0}\left( x \right),x = \left( {{x^{\left( 1 \right)}},...,{x^{\left( n \right)}}} \right) \in {E^n},$$ (2.1) subject to constraints: $${f_i}\left( x \right)\quad 0,\quad i \in \left\{ {1,2, \ldots ,m} \right\} = I;$$ (2.2) $$x \in X\quad \subseteq {E^n},$$
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Subgradient Algorithm on Riemannian Manifolds
Journal of Optimization Theory and Applications, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferreira, O. P., Oliveira, P. R.
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A subgradient method for multiobjective optimization
Computational Optimization and Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
João Xavier da Cruz Neto +3 more
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Accelerating the convergence of subgradient optimisation
European Journal of Operational Research, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barrie M. Baker, Janice Sheasby
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Nondifferentiable Optimisation Subgradient and ε — Subgradient Methods
1976We give some ideas which lead to descent methods for minimizing nondifferentiable functions. Such methods have been published in several papers and they all involve the same concept, namely the e — subdifferential.
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An Incremental Subgradient Method on Riemannian Manifolds
Journal of Optimization Theory and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng Zhang 0036, Gejun Bao
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