Related papers: Set Relations and Approximate Solutions in Set Opt…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
In this paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem. While this paradigm…
This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Sequence optimization, where the items in a list are ordered to maximize some reward has many applications such as web advertisement placement, search, and control libraries in robotics. Previous work in sequence optimization produces a…
To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or…
In the present paper, some aspects of the finite-dimensional theory of set-inclusive generalized equations are studied. Set-inclusive generalized equations are problems arising in several contexts of optimization and variational analysis,…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
We consider the problem of sketching set valuation functions, defined as the expectation of a valuation function applied to independent random item values. For valuation functions that are monotone and either subadditive or submodular, and…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…