Related papers: Linear Superiorization for Infeasible Linear Progr…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We show how to reduce a general, strictly-feasible LP problem, into a min-max problem, which can be solved by the algorithm from the third section of my thesis.
Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety…
Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither…
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…
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…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
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…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solutions that are improved with respect to some secondary…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
The advent of efficient interior point optimization methods has enabled the tractable solution of large-scale linear and nonlinear programming (NLP) problems. A prominent example of such a method is seen in Ipopt, a widely-used, open-source…
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…
Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, super-resolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and…
Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints-compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbations resilience, and…
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe the details and prove the polynomial complexity of the…