Related papers: On the feasibility of generalized inverse linear p…
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…
In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case integration error on the dimension. Roughly speaking, an integration problem is…
We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterising all realisable lists. Although the NIEP…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
Farkas' lemma for semidefinite programming characterizes semidefinite feasibility of linear matrix pencils in terms of an alternative spectrahedron. In the well-studied special case of linear programming, a theorem by Gleeson and Ryan…
Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is…
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…
Inverse optimization involves inferring unknown parameters of an optimization problem from known solutions and is widely used in fields such as transportation, power systems, and healthcare. We study the contextual inverse optimization…
Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…