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Concept

Quasiconvex function

Related publications (24)

Perturbed Utility Stochastic Traffic Assignment

Rui Yao

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

Informs2024

Universal and adaptive methods for robust stochastic optimization

Ali Kavis

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

EPFL2023

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

Volkan Cevher, Ali Kavis, Kimon Antonakopoulos, Leello Tadesse Dadi, Efstratios Panteleimon Skoulakis

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...

2022

Information Retrieval Under Network Uncertainty: Robust Internet Ranking

Ralf Seifert, Anna Timonina-Farkas

Internet ranking algorithms play a crucial role in information technologies and numerical analysis due to their efficiency in high dimensions and wide range of possible applications, including scientometrics and systemic risk in finance (SinkRank, DebtRank ...

2023

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Ahmet Alacaoglu

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

EPFL2021

Yapa: Accelerated Proximal Algorithm For Convex Composite Problems

Mireille El Gheche

Proximal splitting methods are standard tools for nonsmooth optimization. While primal-dual methods have become very popular in the last decade for their flexibility, primal methods may still be preferred for two reasons: acceleration schemes are more effe ...

IEEE2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

A Catalyst Framework for Minimax Optimization

Negar Kiyavash

We introduce a generic two-loop scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated dual problem and takes full advantage of existing ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2020

Random extrapolation for primal-dual coordinate descent

Volkan Cevher, Ahmet Alacaoglu

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, an ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Updates

Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stocha ...

Microtome Publishing2020

Integral Convexity And Parabolic Systems

Bernard Dacorogna

In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...

SIAM PUBLICATIONS2020

Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

Bernard Dacorogna

This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...

SPRINGER2019

An adaptive primal-dual framework for nonsmooth convex minimization

Volkan Cevher, Quoc Tran Dinh, Ahmet Alacaoglu

We propose a new self-adaptive and double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov’s smoothing technique via general Bregman distance functions. It self-adaptiv ...

2020

Stochastic Frank-Wolfe for Composite Convex Minimization

Volkan Cevher, Alp Yurtsever

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...

2019

Scalable Convex Optimization Methods for Semidefinite Programming

Alp Yurtsever

With the ever-growing data sizes along with the increasing complexity of the modern problem formulations, contemporary applications in science and engineering impose heavy computational and storage burdens on the optimization algorithms. As a result, there ...

EPFL2019

Discrete-time regional pole-placement using convex approximations: Theory and application to a boost converter

Emilio Maddalena

The problem of allocating the closed-loop poles of linear systems in specific regions of the complex plane defined by discrete time-domain requirements is addressed. The resulting non-convex set is inner-approximated by a convex region described with linea ...

2019

A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

Volkan Cevher, Quoc Tran Dinh

We propose a new and low per-iteration complexity first-order primal-dual optimization framework for a convex optimization template with broad applications. Our analysis relies on a novel combination of three classic ideas applied to the primal-dual gap fu ...

SIAM Publications2018

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

Complexity Certification of the Fast Alternating Minimization Algorithm for Linear MPC

Colin Neil Jones, Melanie Nicole Zeilinger, Ye Pu

In this technical note, the fast alternating minimization algorithm (FAMA) is proposed to solve model predictive control (MPC) problems with polytopic and second-order cone constraints. Two splitting strategies with efficient implementations for MPC proble ...

2017

Related publications (24)

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021