相关论文: Convexity and multi-dimensional screening for spac…
Myerson's seminal characterization of the revenue-optimal auction for a single item \cite{myerson1981optimal} remains a cornerstone of mechanism design. However, generalizing this framework to multi-item settings has proven exceptionally…
We consider Laplacian eigenfunctions on a $d-$dimensional bounded domain $M$ (or a $d-$dimensional compact manifold $M$) with Dirichlet conditions. These operators give rise to a sequence of eigenfunctions $(e_\ell)_{\ell \in \mathbb{N}}$.…
I study the optimal allocation of positional goods in the presence of externalities arising from consumers' concerns about relative consumption. Applications include luxury goods, priority services, education, and organizational…
We study a general allocation setting where agent valuations are concave additive. In this model, a collection of items must be uniquely distributed among a set of agents, where each agent-item pair has a specified utility. The objective is…
We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…
A principal who values an object allocates it to one or more agents. Agents learn private information (signals) from an information designer about the allocation payoff to the principal. Monetary transfer is not available but the principal…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
The answer to the question posed in the title is yes if the context (the list of variables defining the motion control problem) is dimensionally similar. This article explores the use of the Buckingham $\pi$ theorem as a tool to encode the…
We study a fundamental fair allocation problem, where the agent's value is determined by the number of bins either used to pack or cover the items allocated to them. Fairness is evaluated using the maximin share (MMS) criterion. This…
We consider a class of reinforcement-learning systems in which the agent follows a behavior policy to explore a discrete state-action space to find an optimal policy while adhering to some restriction on its behavior. Such restriction may…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
The problem of fair division of indivisible goods has been receiving much attention recently. The prominent metric of envy-freeness can always be satisfied in the divisible goods setting (see for example \cite{BT95}), but often cannot be…
We give the sharp lower bound of the volume product of three dimensional convex bodies which are invariant under two kinds of discrete subgroups of $O(3)$ of order four. We also characterize the convex bodies with the minimal volume product…
In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller.…
We review several (and provide new) results on the theory of moments, sums of squares and basic semi-algebraic sets when convexity is present. In particular, we show that under convexity, the hierarchy of semidefinite relaxations for…
In a normed linear space X an element x is said to be orthogonal to another element y in the sense of Birkhoff-James, written as $ x \perp_{B}y, $ iff $ \| x \| \leq \| x + \lambda y \| $ for all scalars $ \lambda.$ We prove that a normed…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…