Related papers: Multiplicative Nonholonomic/Newton -like Algorithm
We show that the third order approximation function $M_f$, proposed by S. Amat, S. Busquier, S. Plaza, in \textit{J. Math. Anal. Appl.}, 366(2010), 24--32, for functions $f$ twice continuously differentiable and such that both $f$ and its…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed parameter tractable algorithm that guarantees a…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time…
Single-site Markov Chain Monte Carlo (MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and…