Related Research Articles
In 3D computer graphics, solid objects are usually modeled by polyhedra. A face of a polyhedron is a planar polygon bounded by straight line segments, called edges. Curved surfaces are usually approximated by a polygon mesh. Computer programs for line drawings of opaque objects must be able to decide which edges or which parts of the edges are hidden by an object itself or by other objects, so that those edges can be clipped during rendering. This problem is known as hidden-line removal.
Coarray Fortran (CAF), formerly known as F--, started as an extension of Fortran 95/2003 for parallel processing created by Robert Numrich and John Reid in the 1990s. The Fortran 2008 standard now includes coarrays, as decided at the May 2005 meeting of the ISO Fortran Committee; the syntax in the Fortran 2008 standard is slightly different from the original CAF proposal.
Concurrent computing is a form of computing in which several computations are executed concurrently—during overlapping time periods—instead of sequentially—with one completing before the next starts.
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing everywhere, and lies as close to the observations as possible.
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available.
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
UTEXAS is a slope stability analysis program written by Stephen G. Wright of the University of Texas at Austin. The program is used in the field of civil engineering to analyze levees, earth dams, natural slopes, and anywhere there is concern for mass wasting. UTEXAS finds the factor of safety for the slope and the critical failure surface. Recently the software was used to help determine the reasons behind the failure of I-walls during Hurricane Katrina.
In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects the boundary of P at most twice.
Non-structured programming is the historically earliest programming paradigm capable of creating Turing-complete algorithms. It is often contrasted with the structured programming paradigm, in particular with the use of unstructured control flow using goto statements or equivalent. The distinction was particularly stressed by the publication of the influential "Go To Statement Considered Harmful" open letter in 1968 by Dutch computer scientist Edsger W. Dijkstra, who coined the term "structured programming".
Dimitri Panteli Bertsekas is an applied mathematician, electrical engineer, and computer scientist, a McAfee Professor at the Department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, and also a Fulton Professor of Computational Decision Making at Arizona State University, Tempe.
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier. The augmented Lagrangian is related to, but not identical with, the method of Lagrange multipliers.
NPSOL is a software package that performs numerical optimization. It solves nonlinear constrained problems using the sequential quadratic programming algorithm. It was written in Fortran by Philip Gill of UCSD and Walter Murray, Michael Saunders and Margaret Wright of Stanford University. The name derives from a combination of NP for nonlinear programming and SOL, the Systems Optimization Laboratory at Stanford.
For several years parallel hardware was only available for distributed computing but recently it is becoming available for the low end computers as well. Hence it has become inevitable for software programmers to start writing parallel applications. It is quite natural for programmers to think sequentially and hence they are less acquainted with writing multi-threaded or parallel processing applications. Parallel programming requires handling various issues such as synchronization and deadlock avoidance. Programmers require added expertise for writing such applications apart from their expertise in the application domain. Hence programmers prefer to write sequential code and most of the popular programming languages support it. This allows them to concentrate more on the application. Therefore, there is a need to convert such sequential applications to parallel applications with the help of automated tools. The need is also non-trivial because large amount of legacy code written over the past few decades needs to be reused and parallelized.
In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required to form a monotonic sequence. That is, for a priority queue in which each successively extracted item is the one with the minimum priority, the minimum priority should be monotonically increasing. Conversely for a max-heap the maximum priority should be monotonically decreasing. The assumption of monotonicity arises naturally in several applications of priority queues, and can be used as a simplifying assumption to speed up certain types of priority queues.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
A bucket queue is a data structure that implements the priority queue abstract data type: it maintains a dynamic collection of elements with numerical priorities and allows quick access to the element with minimum priority. In the bucket queue, the priorities must be integers, and it is particularly suited to applications in which the priorities have a small range. A bucket queue has the form of an array of buckets: an array data structure, indexed by the priorities, whose cells contain collections of items with the same priority as each other. With this data structure, insertion of elements and changes of their priority take constant time. Searching for and removing the minimum-priority element takes time proportional to the number of buckets or, by maintaining a pointer to the most recently found bucket, in time proportional to the difference in priorities between successive operations.
SuanShu is a Java math library. It is open-source under Apache License 2.0 available in GitHub. SuanShu is a large collection of Java classes for basic numerical analysis, statistics, and optimization. It implements a parallel version of the adaptive strassen's algorithm for fast matrix multiplication. SuanShu has been quoted and used in a number of academic works.
References
- Schittkowski, Klaus (2014), "NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed and Non-Monotone Line Search", Report
