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A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of…
The support of a vector is the number of nonzero-components. We show that given an integral $m\times n$ matrix $A$, the integer linear optimization problem $\max\left\{\boldsymbol{c}^T\boldsymbol{x} : A\boldsymbol{x} = \boldsymbol{b}, \,…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…
Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed.…
We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a…
This paper presents a finite step method for computing the binary solution to an overdetermined system of linear algebraic equations Ax = b, where A is an m x n real matrix of rank n < m, and b is a real m-vector. The method uses the…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…
Let $\xi$ be a random integer vector, having uniform distribution \[\mathbf{P} \{\xi = (i_1,i_2,...,i_n) = 1/n^n \} \ \hbox{for} \ 1 \leq i_1,i_2,...,i_n\leq n.\] A realization $(i_1,i_2,...,i_n)$ of $\xi$ is called \textit{good}, if its…
The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] . x = 0, where…
This paper introduces a new method for assessing the boundedness and stability of certain vector nonlinear systems with delays and variable coefficients. The approach is based on developing scalar counterparts to the given vector systems.…
We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…