Computational Optimization and Applications

In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function f and a convex (possibly non-smooth ...$$$\mathrm{}$

This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent ...

In this paper, we consider constrained optimization problems with convex objective and smooth convex functional constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve ...$\mathcal{}{}^{\mathrm{}\mathrm{}}$$\mathcal{}{}^{\mathrm{}}$

We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\le d$ orthogonal directions, where d is the dimension of the ambient space. These ...${}^{}$$\mathrm{}\mathrm{}$

In this paper, we propose a method for solving constrained nonsmooth multiobjective optimization problems which is based on a Sequential Quadratic Programming (SQP) type approach and the Gradient Sampling (GS) technique. We consider the ...

Based on the recently introduced Scaled Positive Approximate Karush–Kuhn–Tucker condition for single objective problems, we derive a sequential necessary optimality condition for multiobjective problems with equality and inequality constraints as ...

In this paper, we seek a new modification way to ensure the positiveness of the conjugate parameter and, based on the Dai-Yuan (DY) method in the vector setting, propose an associated family of conjugate gradient (CG) methods with guaranteed ...

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic ...$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$$\sqrt{}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}$$\stackrel{}{\mathcal{}}{}^{\mathrm{}\mathrm{}}{}^{\mathrm{}\mathrm{}}$

The Perron–Frobenius theorem says that the spectral radius of a weakly irreducible nonnegative tensor is the unique positive eigenvalue corresponding to a positive eigenvector. With this fact in mind, the purpose of this paper is to find the ...

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank–Wolfe algorithm and its variants already avoid projections, ...$$$\mathcal{}{}^{\mathrm{}}$

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a robust ...