Related papers: Revisiting the upper bounding process in a safe Br…
It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We present an adaptive safeguarding scheme with a tunable parameter, which we call adaptive gamma-safeguarding,…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…
In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the Newton method when the Newton search directions are…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
Branch and bound algorithms have to cope with several additional difficulties in the multi-objective case. Not only the bounding procedure is considerably weaker, but also the handling of upper and lower bound sets requires much more…
We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and…
Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
Finding optimal solutions for multi-unit combinatorial auctions is a hard problem and finding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
We describe an algorithm based on a logarithmic barrier function, Newton's method, and linear conjugate gradients that obtains an approximate minimizer of a smooth function over the nonnegative orthant. We develop a bound on the complexity…
A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…
Many available formal verification methods have been shown to be instances of a unified Branch-and-Bound (BaB) formulation. We propose a novel machine learning framework that can be used for designing an effective branching strategy as well…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…