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The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
Factors are categorical variables, and the values which these variables assume are called levels. In this paper, we consider the variable selection problem where the set of potential predictors contains both factors and numerical variables.…
The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between \emph{optimization} and…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…
Contemporary large language models are powerful problem-solving tools, but they exhibit weaknesses in their reasoning abilities which ongoing research seeks to mitigate. We investigate graph coloring as a means of evaluating an LLM's…
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
In Noor (2007)[Muhammad Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007) 937-943], proposed an algorithm namely \textbf{Algorithm 2.4} and established a proof to show cubic convergence. The presented…
A factored Nonlinear Program (Factored-NLP) explicitly models the dependencies between a set of continuous variables and nonlinear constraints, providing an expressive formulation for relevant robotics problems such as manipulation planning…
Let U be a universe on n elements, let k be a positive integer, and let F be a family of (implicitly defined) subsets of U. We consider the problems of partitioning U into k sets from F, covering U with k sets from F, and packing k…
We consider the Functional Orientation 2-Color problem, which was introduced by Valiant in his seminal paper on holographic algorithms [SIAM J. Comput., 37(5), 2008]. For this decision problem, Valiant gave a polynomial time holographic…