Related papers: Linear Superiorization for Infeasible Linear Progr…
This paper presents a novel hybrid approach that integrates linear programming (LP) within the loss function of an unsupervised machine learning model. By leveraging the strengths of both optimization techniques and machine learning, this…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
We apply the superiorization methodology to the intensity-modulated radiation therapy (IMRT) treatment planning problem. In superiorization, linear voxel dose inequality constraints are the fundamental modeling tool within which a…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather,…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…
When solving multi-objective programs, the number of objectives essentially determines the computing time. This can even lead to practically unsolvable problems. Consequently, it is worthwhile to reduce the number of objectives without…
This paper proposes an almost feasible Sequential Linear Programming (afSLP) algorithm. In the first part, the practical limitations of previously proposed Feasible Sequential Linear Programming (FSLP) methods are discussed along with…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…