Related papers: Looking for efficiency when avoiding order reducti…
In this paper, we study the numerical solutions of the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
In this paper, we propose two linearized finite difference schemes for solving the logarithmic Schr\"odinger equation (LogSE) without the need for regularization of the logarithmic term. These two schemes employ the first-order and the…
Big data and machine learning methods have become commonplace across economic milieus. One area that has not seen as much attention to these important topics yet is efficiency analysis. We show how the availability of big (wide) data can…
We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
The energy efficiency of analog forms of computing makes it one of the most promising candidates to deploy resource-hungry machine learning tasks on resource-constrained system such as mobile or embedded devices. However, it is well known…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
In this paper, we propose and analyze high order efficient schemes for the time fractional Allen-Cahn equation. The proposed schemes are based on the L1 discretization for the time fractional derivative and the extended scalar auxiliary…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…