Related papers: The regularization continuation method for optimiz…
This paper considers the regularization continuation method and the trust-region updating strategy for the optimization problem with linear equality constraints.The proposed method utilizes the linear conservation law of the regularization…
This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not…
For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact proximal-Newton-type methods, or successive quadratic approximation (SQA) methods, are widely used for their…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
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…
In this article, we consider the residual regularization path-following method with the trust-region updating strategy for the linear complementarity problem. This time-stepping selection based on the trust-region updating strategy…
Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or…
We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
This paper deals with regularized Newton methods, a flexible class of unconstrained optimization algorithms that is competitive with line search and trust region methods and potentially combines attractive elements of both. The particular…
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuous Hessian.…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…