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Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We study some numerical methods for solving second order elliptic problem with interface. We introduce an immersed interface finite element method based on the `broken' $P_1$-nonconforming piecewise linear polynomials on interface…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
Bounded model checking is among the most efficient techniques for the automatic verification of concurrent programs. However, encoding all possible interleavings often requires a huge and complex formula, which significantly limits the…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…
In pure integer linear programming it is often desirable to work with polyhedra that are full-dimensional, and it is well known that it is possible to reduce any polyhedron to a full-dimensional one in polynomial time. More precisely, using…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…