21 papers · ranked by Valyu relevance
Yaguang Yang
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering parameter is usually by heuristics and separate from the selection of the linesearch…
Yin Tat Lee, Santosh Vempala
Theorem 1 (Complementary Slackness). Any x ∈ P and s ∈ D are optimal if and only if x >s = 0. Moreover, if both P and D are non-empty, there exist x ∗ ∈ P and s ∗ ∈ D such that (x ∗ ) >s ∗ = 0 and x ∗ + s ∗ > 0.
Yang, Yaguang
This paper presents a Matlab implementation of an arc-search infeasible interior point algorithm for linear programming (LP), which has a proven polynomial bound of $\mathcal{O}(\sqrt{n}L)$, the best among all interior-point algorithms for LP. Software architecture and major functions are discussed. Its ease of use is…
Frank E. Curtis, Xin Jiang, Qi Wang
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear and/or nonconvex, and when constraint values and derivatives are tractable to…
Filippo Zanetti, Jacek Gondzio
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is applied as a black box with a standard termination criterion which asks for a…
Oliver Serang, Jérémie Bourdon
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a…
Rafal Zdunek, Andrzej Cichocki
Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving large-scale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well…
Charalampos P. Triantafyllidis, Nikolaos Samaras, Sándor Szénási
This paper presents a new simplex-type algorithm for Linear Programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonically improving and (ii) the sequence of these basic solutions is connected with a sequence of…
John W. Pearson, Jacek Gondzio
Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and…
Alemseged Gebrehiwot Weldeyesus, Jacek Gondzio
We are concerned with solving linear programming problems arising in the plastic truss layout optimization. We follow the ground structure approach with all possible connections between the nodal points. For very dense ground structures, the solutions of such problems converge to the so-called generalized Michell…
Jing He, Qi-wei Kong, Ho-Chung Lui, Haitao Liu + 1 more
The definition of factor space and a unified optimization based classification model were developed for linear programming and supervised learning. Intelligent behaviour appeared in a decision process can be treated as a moving point y, the dynamic state observed and controlled by the agent, moving in a factor space…
Stanley E. Strawbridge, Agata Kurowski, Elena Corujo-Simon, Alastair N. Fletcher + 2 more
A crucial aspect of embryology is relating the position of individual cells to the broader geometry of the embryo. A classic example of this is the first cell-fate decision of the mouse embryo, where interior cells become inner cell mass and exterior cells become trophectoderm. Fluorescent labelling, imaging, and…
Agnieszka Prusińska, Krzysztof Szkatuła, Alexey Tret’yakov, José A. Tenreiro Machado + 1 more
'José A. Tenreiro Machado' 'Ivanka Stamova'] This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension…
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…
Thilo Moshagen
Mazurkewicz-Knaster-Kuratowski-Lemma based proof of the Brouwer Fixed-Point Theorem Authors: ['Thilo Moshagen'] In this paper a fixed-point solver for mappings from a Simplex into itself that is gradient-free, global and requires d+1 2 function evaluations for halvening the error is presented. It is based on…
Huan Chen, Ethel Weld, Craig Hendrix, Brian Caffo
The classical Principal Curve algorithm was developed as a nonlinear version of principal component analysis to model curves. However, existing principal curve algorithms with classical penalties, such as smoothness or ridge penalties, lack the ability to deal with complex curve shapes. In this manuscript, we introduce…
Chris Vogl, Peng Zheng, Stephen P. Seslar, Aleksandr Y. Aravkin
We consider the problem of locating a point-source heart arrhythmia using data from a standard diagnostic procedure, where a reference catheter is placed in the heart, and arrival times from a second diagnostic catheter are recorded as the diagnostic catheter moves around within the heart. We model this situation as a…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
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…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…