Related papers: A Refined Algorithm for Curve Fitting by Segmented…

We compute the closest convex piecewise linear-quadratic (PLQ) function with minimal number of pieces to a given univariate piecewise linear-quadratic function. The Euclidean norm is used to measure the distance between functions. First, we…

The idea of dynamic programming (DP), proposed by Bellman in the 1950s, is one of the most important algorithmic techniques. However, in parallel, many fundamental and sequentially simple problems become more challenging, and open to a…

Given n data points in R^d, an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regresssion problems. The graph proposed by Daitch, Kelner and Spielman (ICML~2009) can…

Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

We propose a new method for shape recognition and retrieval based on dynamic programming. Our approach uses the dynamic programming algorithm to compute the optimal score and to find the optimal alignment between two strings. First, each…

We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…

Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…

We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the approximate optimal value function to the…

The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…

Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…

Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…

Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic…

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…

The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…

Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…