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WORHP
WORHP ( "warp", an acronym for "We Optimize Really Huge Problems"), also referred to as eNLP (European NLP solver) by ESA, is a mathematical software library for numerically solving large scale continuous nonlinear optimization problems. WORHP is a hybrid Fortran and C implementation and can be used from C/ C++ and Fortran programs using different interfaces of varying complexity and flexibility. There are also interfaces for the MATLAB, CasADi and AMPL modelling environments. Problem formulation WORHP is designed to solve problems of the form ::: \min_ f(x) :subject to ::: L \leq \begin x \\ g(x) \end \leq U with sufficiently smooth functions f:\R^n \to \R (objective) and g:\R^n \to \R^m (constraints) that may be nonlinear, and need not necessarily be convex. Even problems with large dimensions n and m can be solved efficiently, if the problem is sufficiently sparse. Cases where objective and constraints cannot be evaluated separately, or where constraints can be eva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worhp Banner Final Path
WORHP ( "warp", an acronym for "We Optimize Really Huge Problems"), also referred to as eNLP (European NLP solver) by ESA, is a mathematical software library for numerically solving large scale continuous nonlinear optimization problems. WORHP is a hybrid Fortran and C implementation and can be used from C/ C++ and Fortran programs using different interfaces of varying complexity and flexibility. There are also interfaces for the MATLAB, CasADi and AMPL modelling environments. Problem formulation WORHP is designed to solve problems of the form ::: \min_ f(x) :subject to ::: L \leq \begin x \\ g(x) \end \leq U with sufficiently smooth functions f:\R^n \to \R (objective) and g:\R^n \to \R^m (constraints) that may be nonlinear, and need not necessarily be convex. Even problems with large dimensions n and m can be solved efficiently, if the problem is sufficiently sparse. Cases where objective and constraints cannot be evaluated separately, or where constraints can be eva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMPL
AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems). It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories. AMPL supports dozens of solvers, both open source and commercial software, including CBC, CPLEX, FortMP, MINOS, IPOPT, SNOPT, KNITRO, and LGO. Problems are passed to solvers as nl files. AMPL is used by more than 100 corporate clients, and by government agencies and academic institutions. One advantage of AMPL is the similarity of its syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization. Many modern solvers available on the NEOS Server (formerly hosted at the Argonne National Laboratory, currently hosted at the University of Wisconsin, Madison) accept AMPL input. Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobian Matrix And Determinant
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature. Suppose is a function such that each of its first-order partial derivatives exist on . This function takes a point as input and produces the vector as output. Then the Jacobian matrix of is defined to be an matrix, denoted by , whose th entry is \mathbf J_ = \frac, or explicitly :\mathbf J = \begin \dfrac & \cdots & \dfrac \end = \begin \nabla^ f_1 \\ \vdots \\ \nabla^ f_m \end = \begin \dfrac & \cdots & \dfrac\\ \vdots & \ddots & \vdots\\ \dfrac & \cdots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bremen
The University of Bremen (German: ''Universität Bremen'') is a public university in Bremen, Germany, with approximately 23,500 people from 115 countries. It is one of 11 institutions which were successful in the category "Institutional Strategies" of the Excellence Initiative launched by the Federal Government and the Federal States in 2012. The university was also successful in the categories "Graduate Schools" and "Clusters of Excellence" of the initiative. Some of the paths that were taken in the early days of the university, also referred to as the "Bremen model", have since become characteristics of modern universities, such as interdisciplinary, explorative learning, social relevance to practice-oriented project studies which enjoy a high reputation in the academic world as well as in business and industry. History Though Bremen became a university city only recently, higher education in Bremen has a long tradition. The Bremen Latin School was upgraded to "Gymnasium Acad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Space Research And Technology Centre
The European Space Research and Technology Centre (ESTEC) is the European Space Agency's main technology development and test centre for spacecraft and space technology. It is situated in Noordwijk, South Holland, in the western Netherlands, although several kilometers off the village but immediately linked to the most Northern district of the nearby town Katwijk. At ESTEC, about 2500 engineers, technicians and scientists work hands-on with mission design, spacecraft and space technology. ESTEC provides extensive testing facilities to verify the proper operation of spacecraft, such as the Large Space Simulator (LSS), acoustic and electromagnetic testing bays, multi-axis vibration tables and the ESA Propulsion Laboratory (EPL). Prior to launch, almost all of the equipment that ESA launches is tested in some degree at ESTEC. The Space Expo is ESTEC's visitors centre. It has a permanent exhibition about space exploration. Activities * Future mission assessment * Current project su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Aerospace Center
The German Aerospace Center (german: Deutsches Zentrum für Luft- und Raumfahrt e.V., abbreviated DLR, literally ''German Center for Air- and Space-flight'') is the national center for aerospace, energy and transportation research of Germany, founded in 1969. It is headquartered in Cologne with 35 locations throughout Germany. The DLR is engaged in a wide range of research and development projects in national and international partnerships. DLR also acts as the German space agency and is responsible for planning and implementing the German space programme on behalf of the German federal government. As a project management agency, DLR coordinates and answers the technical and organisational implementation of projects funded by a number of German federal ministries. As of 2020, the German Aerospace Center had a national budget of €1.261 billion. Overview DLR has approximately 10.000 employees at 30 locations in Germany. Institutes and facilities are spread over 13 sites, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active Set
In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An optimization problem is defined using an objective function to minimize or maximize, and a set of constraints : g_1(x) \ge 0, \dots, g_k(x) \ge 0 that define the feasible region, that is, the set of all ''x'' to search for the optimal solution. Given a point x in the feasible region, a constraint : g_i(x) \ge 0 is called active at x_0 if g_i(x_0) = 0, and inactive at x if g_i(x_0) > 0. Equality constraints are always active. The active set at x_0 is made up of those constraints g_i(x_0) that are active at the current point . The active set is particularly important in optimization theory, as it determines which constraints will influence the final result of optim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Point Method
Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems that were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Quadratic Programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable. SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to Newton's method for finding a point where the gradient of the objective vanishes. If the problem has only equality constraints, then the method is equivalent to applying Newton's method to the first-order optimality conditions, or Karush–Kuhn–Tucker conditions, of the problem. Algorithm basics Consider a nonlinear programming problem of the form: :\begin \min\limits_ & f(x) \\ \mbox & b(x) \ge 0 \\ & c(x) = 0. \end The Lagrangian for this problem is :\mathcal(x,\lambda,\sigma) = f(x) - \lambda b(x) - \sigma c(x), wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Colouring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color. Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as-is. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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