Related papers: Discrete choice prox-functions on the simplex
We construct new families of direct serendipity and direct mixed finite elements on general planer convex polygons that are $H^1$ and $H(div)$ conforming, respectively, and possess optimal order of accuracy for any order. They have a…
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…
We provide sharp and explicit characterizations of the normal cone to sublevel sets of suprema of arbitrary functions, expressed exclusively in terms of subdifferentials of the data functions. In the convex case, the resulting formulas…
In this paper we derive locally D-optimal designs for discrete choice experiments based on multinomial probit models. These models include several discrete explanatory variables as well as a quantitative one. The commonly used multinomial…
It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
We study the consumption behaviour of an asymmetric network of heterogeneous agents in the framework of discrete choice models with stochastic decision rules. We assume that the interactions among agents are uniquely specified by their…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We study the properties of input-consuming derivations of moded logic programs. Input-consuming derivations can be used to model the behavior of logic programs using dynamic scheduling and employing constructs such as delay declarations. We…
Model training algorithms which observe a small portion of the training set in each computational step are ubiquitous in practical machine learning, and include both stochastic and online optimization methods. In the vast majority of cases,…
The learning of predictive models for data-driven decision support has been a prevalent topic in many fields. However, construction of models that would capture interactions among input variables is a challenging task. In this paper, we…
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…