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We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
This paper takes an empirical look at asymptotic runtime growth rates for the most widely used algorithms for solving linear programming (LP) problems across a set of six optimization application areas that are known to produce large and…
Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
The TOP-IMPLART project consists of the design and implementation of a linear proton accelerator, its control and monitoring systems for the treatment of superficial and semi-deep tumors. The energy of 150 MeV (corresponding to a…
Large language models are thought to have the potential to aid in medical decision making. This work investigates the degree to which this might be the case. We start with the treatment problem, the patient's core medical decision-making…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial…
The introduction of 5G networks has significantly advanced communication technology, offering faster speeds, lower latency, and greater capacity. This progress sets the stage for Beyond 5G (B5G) networks, which present new complexity and…
Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
The Maximum Satisfiability problem (MaxSAT) is a major optimization challenge with numerous practical applications. In recent MaxSAT evaluations, most MaxSAT solvers have incorporated an Integer Linear Programming (ILP) solver into their…
We investigate the feasibility problem for generalized inverse linear programs. Given an LP with affinely parametrized objective function and right-hand side as well as a target set Y, the goal is to decide whether the parameters can be…
Radiation therapy is considered to be one of important treatment protocols for cancers. Radiation therapy employs several beams of ionizing radiation to kill cancer tumors, but such irradiation also causes damage to normal tissues.…