Related papers: Analytic Center Cutting Plane Methods for Variatio…

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…

We address the issue of generating cutting planes for mixed integer programs from multiple rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of the simplex tableau is an intersection cuts from a…

Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…

For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…

The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…

We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Chvatal-Gomory cutting planes (CG-cuts for short) are a fundamental tool in Integer Programming. Given any single CG-cut, one can derive an entire family of CG-cuts, by `iterating' its multiplier vector modulo one. This leads naturally to…

Clinically useful proton Computed Tomography images will rely on algorithms to find the three-dimensional proton stopping power distribution that optimally fits the measured proton data. We present a least squares iterative method with many…

Binary segmentation of volumetric images of porous media is a crucial step towards gaining a deeper understanding of the factors governing biogeochemical processes at minute scales. Contemporary work primarily revolves around primitive…

This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…

Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or…

We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points…

We propose a disciplined, numerically stable, and scalable approach to SDP relaxations of the ACOPF problem based on linear cutting-planes. Our method can be warm-started and, owing to its linear nature, enables the computation of tight and…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…