Related papers: Hybrid algorithms without the extra-steps for equi…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
Hybrid optimization algorithms have gained popularity as it has become apparent there cannot be a universal optimization strategy which is globally more beneficial than any other. Despite their popularity, hybridization frameworks require…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
Embedded optimization-based planning for hybrid systems is challenging due to the use of mixed-integer programming, which is computationally intensive and often sensitive to the specific numerical formulation. To address that challenge,…
In this paper we present new stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions. To obtain error estimates without elliptic regularity assumptions, we…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud…
Gradient methods have applications in multiple fields, including signal processing, image processing, and dynamic systems. In this paper, we present a nonlinear gradient method for solving convex supra-quadratic functions by developing the…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…
We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast…