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We consider a class of problems related to variable knockout, where knockout means set a variable to zero. Given an optimisation problem formulated as a zero-one integer program the question we consider in this paper is what might be an…
Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
This study introduces an approach to obtain a neighboring extremal optimal control (NEOC) solution for a closed-loop optimal control problem, applicable to a wide array of nonlinear systems and not necessarily quadratic performance indices.…
We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local…
Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…