相关论文: Max-Min Representation of Piecewise Linear Functio…
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of…
We show how to reduce a general, strictly-feasible LP problem, into a min-max problem, which can be solved by the algorithm from the third section of my thesis.
Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…
We prove tight upper bounds for the number of vertices of a simple polygon that is the union or the intersection of two simple polygons with given numbers of convex and concave vertices. The similar question on graphs of the lower (or…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be…
It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…
Signed Minkowski decomposition is an expression of a polytope as a Minkowski sum and difference of smaller polytopes. Signed Minkowski decompositions of a polytope can be interpreted as factorizations of a max-plus (tropical) function. We…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…
Mixed integer linear programming (MILP) has seen a sharp rise in use for engineering optimization applications in recent years. Even for initially non-linear problems, it is often the method of choice. Then, the non-linear functions have to…
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…
Let X be a linearly ordered set of arbitrary size (finite or infinite). Natural functions on such a set one can define using the linear order include maximum, minimum and median functions. While it is clear what the clone generated by the…
Function graphs are graphs representable by intersections of continuous real-valued functions on the interval [0,1] and are known to be exactly the complements of comparability graphs. As such they are recognizable in polynomial time.…
An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…