Related papers: On Huang and Noor's Open Problem
We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input…
This paper extends split variational inclusion problems to dynamic, stochastic, and multi-agent systems in Banach spaces. We propose novel iterative algorithms to handle stochastic noise, time-varying operators, and coupled variational…
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…
Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a simplicial homology computation. Like…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We…
This article presents a compact implementation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
This paper proposes a novel and simple algorithm of facet enumeration for convex polytopes. The complexity of the algorithm is discussed. The algorithm is implemented in Matlab. Some simple polytopes with known H-representations and…