Related papers: A combinatorial algorithm for constrained assortme…
Recommendation systems when employed in markets play a dual role: they assist users in selecting their most desired items from a large pool and they help in allocating a limited number of items to the users who desire them the most. Despite…
We study the active learning problem of top-$k$ ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the top-$k$ items with high probability by adaptively querying sets for comparisons and…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
We study the quadratic resource allocation problem and its variant with lower and upper constraints on nested sums of variables. This problem occurs in many applications, in particular battery scheduling within decentralized energy…
The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We…
In computer science, sorting algorithms are crucial for data processing and machine learning. Large datasets and high efficiency requirements provide challenges for comparison-based algorithms like Quicksort and Merge sort, which achieve…
This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
The apportionment problem deals with the fair distribution of a discrete set of $k$ indivisible resources (such as legislative seats) to $n$ entities (such as parties or geographic subdivisions). Highest averages methods are a frequently…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
The Bin Packing Problem is one of the most important Combinatorial Optimization problems in optimization and has a lot of real-world applications. Many approximation algorithms have been presented for this problem because of its NP-hard…
We study the assortment optimization problem under the Sequential Multinomial Logit (SML), a discrete choice model that generalizes the multinomial logit (MNL). Under the SML model, products are partitioned into two levels, to capture…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…