18 papers · ranked by Valyu relevance
Andreas Löhne
We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping F : R n ⇒ R q with polyhedral convex graph with respect to a set ordering relation which is generated by a polyhedral convex cone C ⊆ R q . The method is proven to be correct and finite…
Daniel Ciripoi, Andreas Löhne, Benjamin Weißing
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for one convex polyhedron are, for example, the polar, the conical hull and the image…
Arun L. Gain, Gláucio H. Paulino, Leonardo S. Duarte, Ivan F. M. Menezes
'Ivan F. M. Menezes'] Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the unstructured nature and the facial connectivity between elements…
Steffen Borgwardt, Charles Viss
Circuits play a fundamental role in polyhedral theory and linear programming. For instance, circuits are used as step directions in various augmentation schemes for solving linear programs or to leave degenerate vertices while running the simplex method. However, there are significant challenges when implementing these…
Camille Coti, David Monniaux, Hang Yu
A convex polyhedron, or polyhedron for short here, in dimension n is the solution set over Qn (or, equivalently, R n ) of a system of inequalities (with integer or rational coefficients). Polyhedra in higher dimension are typically used to enclose the reachable states of systems whose state can be expressed, at least…
William Pettersson, Melih Özlen
This paper introduces the first objective space algorithm which can exactly find all supported and non-supported non-dominated solutions to a mixed-integer multi-objective linear program with an arbitrary number of objective functions. This algorithm is presented in three phases. First it builds up a super-set which…
Karim Hammoudi, Fadi Dornaika
This paper presents a model-based approach for reconstructing 3D polyhedral building models from aerial images. The proposed approach exploits some geometric and photometric properties resulting from the perspective projection of planar structures. Data are provided by calibrated aerial images. The novelty of the…
Stefan Müller, Georg Regensburger
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This…
Yuanpeng Liu, Ting-Uei Lee, Anooshe Rezaee Javan, Yi Min Xie
Goldberg polyhedra have been widely studied across multiple fields, as their distinctive pattern can lead to many useful applications. Their topology can be determined using Goldberg’s method through generating topologically equivalent structures, named cages. However, the geometry of Goldberg polyhedra remains…
Haibin Chen, Hong Zhi Yan, Guanglu Zhou
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on reformulating polynomial optimization problems (POPs) as conic programs over the cone of…
Rahib H. Abiyev, Mustafa Tunay
A novel learning algorithm for solving global numerical optimization problems is proposed. The proposed learning algorithm is intense stochastic search method which is based on evaluation and optimization of a hypercube and is called the hypercube optimization (HO) algorithm. The HO algorithm comprises the…
Alena Khmelinskaia, Neville P. Bethel, Farzad Fatehi, Aleksandar Antanasijevic + 15 more
Many naturally occurring protein assemblies have dynamic structures that allow them to perform specialized functions. For example, clathrin coats adopt a wide variety of architectures to adapt to vesicular cargos of various sizes. Although computational methods for designing novel self-assembling proteins have advanced…
Ksenia Bestuzheva, Ambros Gleixner, Helena Völker
Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since the computational cost depends only on the number of terms in the polynomials…
Paula C. Sanematsu
The development of physics-based 3D models that investigate the behavior of biological tissues requires effective and efficient visualization tools. The open-source software ParaView has such capabilities, but often impose a steep learning curve due to the use of the Visualization Toolkit (VTK) data structures. To…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Authors not listed
With the ever-increasing demand for atomistic structures representative of real-life systems as well as the ad-vent of exascale computers, it has now become necessary and possible to use advanced global optimization (GO) techniques to intelligently sample the potential energy surface (PES). Given the previous studies…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Authors not listed
This article presents an overview about the state of the art in the development of structured packings for distillation applications. The focus is on highlighting different approaches including heuristic development cycles, the development of new packing structures, 3D-printing as tool for manufacturing, and…