相关论文: A new class of smoothing methods for mathematical …

We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…

The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP)…

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…

This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…

The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…

A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…

An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…

Mathematical programs with or-constraints form a new class of disjunctive optimization problems with inherent practical relevance. In this paper, we provide a comparison of three different first-order methods for the numerical treatment of…

We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…

We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth…

We present a unified theorem for the convergence analysis of stochastic gradient algorithms for minimizing a smooth and convex loss plus a convex regularizer. We do this by extending the unified analysis of Gorbunov, Hanzely \& Richt\'arik…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…