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We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
The mechanical response of transparent materials to optical forces is a topic that concerns a wide range of fields, from the manipulation of biological material by optical tweezers to the design of nano-optomechanical systems (NOMS).…
The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the…
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the…
In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores…
In this paper, we propose a framework for solving a class of optimization problems encountered in a range of power allocation problems in wireless relay networks. In particular, power allocation for weighted sum-rate and common-rate…
The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate,…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
We present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time-varying connectivity. Our framework is general in that this value can represent a consensus…
Neural abstractive summarization models are flexible and can produce coherent summaries, but they are sometimes unfaithful and can be difficult to control. While previous studies attempt to provide different types of guidance to control the…
Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This…
This study addresses the interpretable estimation of price bounds in the context of price optimization. In recent years, price-optimization methods have become indispensable for maximizing revenue and profits. However, effective application…
Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…
Exclusion and shape restrictions play a central role in defining causal effects and interpreting estimates in potential outcomes models. To date, the testable implications of such restrictions have been studied on a case-by-case basis in a…
Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…