Related papers: Convex Choice
This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…
Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
The amount of information in the form of features and variables avail- able to machine learning algorithms is ever increasing. This can lead to classifiers that are prone to overfitting in high dimensions, high di- mensional models do not…
We use the United States Supreme Court as an illuminative context in which to discuss three different spatial voting preference models: an instance of the widely used single-peaked preferences, and two models that are more novel in which…
We study the problem of networked online convex optimization, where each agent individually decides on an action at every time step and agents cooperatively seek to minimize the total global cost over a finite horizon. The global cost is…
We consider the optimal risk sharing problem with a continuum of agents, modeled via a non-atomic measure space. Individual preferences are not assumed to be convex. We show the multiplicity of agents induces the value function to be…
This paper proposes a model of choice via agentic artificial intelligence (AI). A key feature is that the AI may misinterpret a menu before recommending what to choose. A single acyclicity condition guarantees that there is a monotonic…
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
Many data sets consist of variables with an inherent group structure. The problem of group selection has been well studied, but in this paper, we seek to do the opposite: our goal is to select at least one variable from each group in the…
Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…
Discrete Lossless Convexification (DLCvx) formulates a convex relaxation for a specific class of discrete-time non-convex optimal control problems. It establishes sufficient conditions under which the solution of the relaxed problem…
We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along three main lines. First, if $d$ represents the doubling dimension of the…
We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis…
In many clinical trials, individuals in different subgroups have experience differential treatment effects. This leads to individualized differences in treatment benefit. In this article, we introduce the general concept of predictive…
In this paper we study a dynamic vehicle routing problem in which there are multiple vehicles and multiple classes of demands. Demands of each class arrive in the environment randomly over time and require a random amount of on-site service…
It is obtained a natural generalisation of Uspenskij's selection characterisation of paracompact $C$-spaces. The method developed to achieve this result is also applied to give a simplified proof of a similar characterisation of paracompact…
From a geometric viewpoint, billiard trajectories and geodesics are related by mutual approximation results. In one direction, it is known that every geodesic curve in the boundary of a smooth convex body can be approximated by a sequence…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…