Separately Convex and Separately Continuous Preferences: On Results of Schmeidler, Shafer, and Bergstrom-Parks-Rader
We provide necessary and sufficient conditions for a correspondence taking values in a finite-dimensional Euclidean space to be open so as to revisit the pioneering work of Schmeidler (1969), Shafer (1974), Shafer-Sonnenschein (1975) and Bergstrom-Rader-Parks (1976) to answer several questions they and their followers left open. We introduce the notion of separate convexity for a correspondence and use it to relate to classical notions of continuity while giving salience to the notion of separateness as in the interplay of separate continuity and separate convexity of binary relations. As such, we provide a consolidation of the convexity-continuity postulates from a broad inter-disciplinary perspective and comment on how the qualified notions proposed here have implications of substantive interest for choice theory.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Real-Time Systems Optimization with Black-box Constraints and Hybrid Variables
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the o…
A Convex Surrogate Operator for General Non-Modular Loss Functions
Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tig…
Sensor Selection by Linear Programming
We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as …
Computational EfficiencyLocally Regularized Sparse Graph by Fast Proximal Gradient Descent
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric informat…
ClusteringMulti-Model Federated Learning with Provable Guarantees
Federated Learning (FL) is a variant of distributed learning where edge devices collaborate to learn a model without sharing their data with the central server or each other. We refer to the process of training multiple …
Federated Learningmodel