相关论文: NCVX: A User-Friendly and Scalable Package for Non…

Pairwise learning is receiving increasing attention since it covers many important machine learning tasks, e.g., metric learning, AUC maximization, and ranking. Investigating the generalization behavior of pairwise learning is thus of…

Global solvers have emerged as a powerful paradigm for 3D vision, offering certifiable solutions to nonconvex geometric optimization problems traditionally addressed by local or heuristic methods. This survey presents the first systematic…

This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…

Feature selection in learning to rank has recently emerged as a crucial issue. Whereas several preprocessing approaches have been proposed, only a few works have been focused on integrating the feature selection into the learning process.…

We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…

This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with…

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal…

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming…

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…

In a recent study, Ansary (Optim Methods Softw 38(3):570-590,2023) proposed a Newton-type proximal gradient method for nonlinear multiobjective optimization problems (NPGMO). However, the favorable convergence properties typically…

In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…

Cluster resource allocation is a multidimensional search problem that finds the best allocation of tasks to servers. Because the search space grows exponentially, modern approaches frame it as a mixed integer program (MIP) or a complex set…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…

Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic…

Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…

In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an…

Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the…