Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions
نویسندگان
چکیده
We study mixed-integer nonlinear optimization (MINLO) formulations of the disjunction $$x\in \{0\}\cup [\ell ,u]$$ , where z is a binary indicator for ( $$0 \le \ell 1$$
منابع مشابه
ANOVA decomposition of convex piecewise linear functions
Piecewise linear convex functions arise as integrands in stochastic programs. They are Lipschitz continuous on their domain, but do not belong to tensor product Sobolev spaces. Motivated by applying Quasi-Monte Carlo methods we show that all terms of their ANOVA decomposition, except the one of highest order, are smooth if the underlying densities are smooth and a certain geometric condition is...
متن کاملExplicit Univariate Global Optimization with Piecewise Linear Support Functions
Piecewise linear convex and concave support functions combined with Pijavskii’s method are proposed to be used for solving global optimization problems. Rules for constructing support functions are introduced.
متن کاملPiecewise Convex Function Estimation: Pilot Estimators
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model selection problem is to determine the number of convexity change points. For kernel estimates in Gaussian noise, the number of false change points is evaluated as a...
متن کاملComputing the conjugate of convex piecewise linear-quadratic bivariate functions
We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and fac...
متن کاملConvex piecewise-linear fitting
We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2022
ISSN: ['0022-3239', '1573-2878']
DOI: https://doi.org/10.1007/s10957-022-02144-6