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In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…
In this paper we consider constrained optimization problems where both the objective and constraint functions are of the black-box type. Furthermore, we assume that the nonlinear inequality constraints are non-relaxable, i.e. their values…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…
With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications…
Line features are valid complements for point features in man-made environments. 3D-2D constraints provided by line features have been widely used in Visual Odometry (VO) and Structure-from-Motion (SfM) systems. However, how to accurately…
We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…
We consider the case of derivative-free algorithms for non-convex optimization, also known as zero order algorithms, that use only function evaluations rather than gradients. For a wide variety of gradient approximators based on finite…
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 graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…
In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…