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Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…
The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…
This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and…
We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order…
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…
The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…