相关论文: A new nonmonotone adaptive trust region algorithm

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…

This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…

In this paper, two types of nonmonotone memory gradient algorithm for solving unconstrained multiobjective optimization problems are introduced. Under some suitable conditions, we show the convergence of the full sequence generated by the…

We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…

Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…

Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive…

We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various…

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine…

In this work we propose a general nonmonotone line-search method for nonconvex multi\-objective optimization problems with convex constraints. At the $k$th iteration, the degree of nonmonotonicity is controlled by a vector $\nu_{k}$ with…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…

We present a new solution framework to solve the generalized trust region subproblem (GTRS) of minimizing a quadratic objective over a quadratic constraint. More specifically, we derive a convex quadratic reformulation (CQR) via minimizing…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

Model-based derivative-free optimization (DFO) methods are an important class of DFO methods that are known to struggle with solving high-dimensional optimization problems. Recent research has shown that incorporating random subspaces into…

Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…

We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A…