Piecewise affine functions and polyhedral sets∗

DOI10.1080/02331939408844018zbMath0816.49011OpenAlexW1996833224MaRDI QIDQ4764843

O. I. Zor'Ko, Valentin V. Gorokhovik

Publication date: 2 July 1995

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: http://elib.bsu.by/handle/123456789/12813

zbMATH Keywords

polyhedral setsepigraphhypographpolyhedral functionspiecewise affine and piecewise linear functions

Mathematics Subject Classification ID

Variational inequalities (49J40) Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and function-space-valued mappings on manifolds (58C06)

Related Items (19)

Locally piecewise affine functions and their order structure ⋮ Saddle representations of positively homogeneous functions by linear functions ⋮ Unnamed Item ⋮ Positively homogeneous functions revisited ⋮ Geometrical and analytical characteristic properties of piecewise affine mappings ⋮ On optimization of stochastic max-min-plus-scaling systems -- an approximation approach ⋮ Representations of continuous piecewise affine functions ⋮ Finding the set of global minimizers of a piecewise affine function ⋮ Nonlocal error bounds for piecewise affine functions ⋮ MorphoActivation: generalizing ReLU activation function by mathematical morphology ⋮ Quasidifferntiability of optimal solutions in parametric optimal solutions in parametric nonlinear optimization ⋮ DCA-based algorithms for DC fitting ⋮ An algorithm for the estimation of a regression function by continuous piecewise linear functions ⋮ MPC for continuous piecewise-affine systems ⋮ Minimal convex majorants of functions and Demyanov–Rubinov exhaustive super(sub)differentials ⋮ New global optimality conditions for nonsmooth DC optimization problems ⋮ A difference of convex optimization algorithm for piecewise linear regression ⋮ Compensated convexity and Hausdorff stable geometric singularity extractions ⋮ The method of codifferential descent for convex and global piecewise affine optimization

Cites Work

• On the expressibility of piecewise-linear continuous functions as the difference of two piecewise-linear convex functions
• Optimization and nonsmooth analysis
• On locally-Lipschitz quasi-differentiate functions in Banach-spaces
• ε-Quasidifferentiability of real-valued functions and optimality conditions in extremal problems
• Piecewise affine functions as a difference of two convex functions
• Elementary Differential Topology. (AM-54)
• Convex Analysis
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