Related papers: Global convergence of a BFGS-type algorithm for no…
In this paper, a modification to the Gradient Sampling (GS) method for minimizing nonsmooth nonconvex functions is presented. One drawback in GS method is the need of solving a Quadratic optimization Problem (QP) at each iteration, which is…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex…
This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective…
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear…
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
L-BFGS is the state-of-the-art optimization method for many large scale inverse problems. It has a small memory footprint and achieves superlinear convergence. The method approximates Hessian based on an initial approximation and an update…
We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper presents a new generalized Armijo's line-search method, and combines it with a phi-regulation defined to obtain a new algorithm solving the very general non-linear non-smooth convex programming. For the algorithm designed, the…
This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain…