A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions
نویسندگان
چکیده
منابع مشابه
Computing 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 کاملANOVA 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 کاملThe piecewise linear-quadratic model for computational convex analysis
A new computational framework for computer-aided convex analysis is proposed and investigated. Existing computational frameworks are reviewed and their limitations pointed out. The class of piecewise linear-quadratic functions is introduced to improve convergence and stability. A stable convex calculus is achieved using symbolic-numeric algorithms to compute all fundamental transforms of convex...
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 کاملnetwork optimization with piecewise linear convex costs
the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...
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: Computational Optimization and Applications
سال: 2018
ISSN: 0926-6003,1573-2894
DOI: 10.1007/s10589-018-0007-1