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This paper focuses on the minimization of a sum of a twice continuously differentiable function f and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of f involving the $\varrho$th ...$\mathrm{}$$\mathrm{}\mathrm{}$$\mathrm{}$$$${}_{\mathrm{}}$

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear ...

In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, ...

We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. ...

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 ...${}^{}$${}^{}$${}^{}$

We extend and analyze the trust region method for solving smooth and unconstrained multicriteria optimization problems on Riemannian manifolds. At each iteration of this method, a quadratic model is assigned to each component of the vectorial ...

We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new ...

We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic ...

This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To ...

We introduce a perturbed augmented Lagrangian method framework, which is a convenient tool for local analyses of convergence and rates of convergence of some modifications of the classical augmented Lagrangian algorithm. One example to which our ...

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate ...

This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is ...

In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of ...

Least squares form one of the most prominent classes of optimization problems with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must account for nonlinear ...

Recently, in a series of papers [Y. Rahimi, C. Wang, H. Dong, and Y. Lou, SIAM J. Sci. Comput., 41 (2019), pp. A3649--A3672; C. Wang, M. Tao, J. Nagy, and Y. Lou, SIAM J. Imaging Sci., 14 (2021), pp. 749--777; C. Wang, M. Yan, and Y. Lou, IEEE ...

Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic, and constraint ...

We extend a sequential quadratic programming method for equality constrained optimization to the setting of Hilbert manifolds. The use of retractions and linearizing maps allows us to pull back the functional and the constraint mapping to linear spaces ...

In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem ...

This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: where one minimizes an objective that can be written as the composition of a convex function with one that is continuiously ...

In this paper, we propose a new sequential quadratic optimization algorithm for solving two-block nonconvex optimization with linear equality and generalized box constraints. First, the idea of the splitting algorithm is embedded in the method for ...