Publications related to Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

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

Integrating advanced discrete choice models in mixed integer linear optimization

Michel Bierlaire, Bernard Gendron

In many transportation systems, a mismatch between the associated design and planning decisions and the demand is typically encountered. A tailored system is not only appealing to operators, which could have a better knowledge of their operational costs, b ...

PERGAMON-ELSEVIER SCIENCE LTD2021

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

Efficient Relaxations for Dense CRFs with Sparse Higher-Order Potentials

Mathieu Salzmann

Dense conditional random fields (CRFs) have become a popular framework for modeling several problems in computer vision such as stereo correspondence and multiclass semantic segmentation. By modeling long-range interactions, dense CRFs provide a labeling t ...

SIAM PUBLICATIONS2019

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Daniel Kuhn, Napat Rujeerapaiboon, Kilian Schindler, Wolfram Wiesemann

Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier-detection and clustering problem, which assigns a prescribed number of datapoints to ...

2019

Sampling can be faster than optimization

Nicolas Henri Bernard Flammarion

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...

PNAS2019

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

A Lagrangian relaxation technique for the demand-based benefit maximization problem

Michel Bierlaire, Shadi Sharif Azadeh, Virginie Janine Camille Lurkin, Meritxell Pacheco Paneque, Bernard Gendron

The integration of discrete choice models with Mixed Integer Linear Programming (MILP) models provides a better understanding of customers' preferences to operators while planning for their systems. However, the formulations associated with the former are ...

2018

Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

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A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

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

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

Integrating advanced discrete choice models in mixed integer linear optimization

Stochastic Frank-Wolfe for Composite Convex Minimization

Efficient Relaxations for Dense CRFs with Sparse Higher-Order Potentials

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Sampling can be faster than optimization

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

A Lagrangian relaxation technique for the demand-based benefit maximization problem

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

Integrating advanced discrete choice models in mixed integer linear optimization

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

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

Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization

Stochastic Frank-Wolfe for Composite Convex Minimization

Sampling can be faster than optimization

Efficient Relaxations for Dense CRFs with Sparse Higher-Order Potentials

A Lagrangian relaxation technique for the demand-based benefit maximization problem

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials