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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Active set method ： ウィキペディア英語版 :''"Active Set" redirects here. For the Wikipedia article on the band, see The Active Set.''In mathematical optimization, a 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 0is called active at x if g_i(x)=0 and inactive at x if g_i(x)>0. Equality constraints are always active. The active set at x is made up of those constraints g_i(x) 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 optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. ==Active set methods==In general an active set algorithm has the following structure::Find a feasible starting point:repeat until "optimal enough"::''solve'' the equality problem defined by the active set (approximately)::''compute'' the Lagrange multipliers of the active set::''remove'' a subset of the constraints with negative Lagrange multipliers::''search'' for infeasible constraints:end repeatMethods that can be described as active set methods include:* Successive linear programming (SLP) * Sequential quadratic programming (SQP) * Sequential linear-quadratic programming (SLQP) * Reduced gradient method (RG) * Generalized reduced gradient method (GRG) :''"Active Set" redirects here. For the Wikipedia article on the band, see The Active Set.'' In mathematical optimization, a problem is defined using an objective function to minimize or maximize, and a set of constraints :$g\_1(x)\backslash ge\; 0,\; \backslash dots,\; g\_k(x)\backslash ge\; 0$ 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 :$g\_i(x)\; \backslash ge\; 0$ is called active at $x$ if $g\_i(x)=0$ and inactive at $x$ if $g\_i(x)>0.$ Equality constraints are always active. The active set at $x$ is made up of those constraints $g\_i(x)$ 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 optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. ==Active set methods== In general an active set algorithm has the following structure: :Find a feasible starting point :repeat until "optimal enough" ::''solve'' the equality problem defined by the active set (approximately) ::''compute'' the Lagrange multipliers of the active set ::''remove'' a subset of the constraints with negative Lagrange multipliers ::''search'' for infeasible constraints :end repeat Methods that can be described as active set methods include: * Successive linear programming (SLP) * Sequential quadratic programming (SQP) * Sequential linear-quadratic programming (SLQP) * Reduced gradient method (RG) * Generalized reduced gradient method (GRG) 抄文引用元・出典: フリー百科事典『 active at x if g_i(x)=0 and inactive at x if g_i(x)>0. Equality constraints are always active. The active set at x is made up of those constraints g_i(x) 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 optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. ==Active set methods==In general an active set algorithm has the following structure::Find a feasible starting point:repeat until "optimal enough"::''solve'' the equality problem defined by the active set (approximately)::''compute'' the Lagrange multipliers of the active set::''remove'' a subset of the constraints with negative Lagrange multipliers::''search'' for infeasible constraints:end repeatMethods that can be described as active set methods include:* Successive linear programming (SLP) * Sequential quadratic programming (SQP) * Sequential linear-quadratic programming (SLQP) * Reduced gradient method (RG) * Generalized reduced gradient method (GRG) ">ウィキペディア（Wikipedia）』 ■active at x if g_i(x)=0 and inactive at x if g_i(x)>0. Equality constraints are always active. The active set at x is made up of those constraints g_i(x) 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 optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. ==Active set methods==In general an active set algorithm has the following structure::Find a feasible starting point:repeat until "optimal enough"::''solve'' the equality problem defined by the active set (approximately)::''compute'' the Lagrange multipliers of the active set::''remove'' a subset of the constraints with negative Lagrange multipliers::''search'' for infeasible constraints:end repeatMethods that can be described as active set methods include:* Successive linear programming (SLP) * Sequential quadratic programming (SQP) * Sequential linear-quadratic programming (SLQP) * Reduced gradient method (RG) * Generalized reduced gradient method (GRG) ">ウィキペディアで「:''"Active Set" redirects here. For the Wikipedia article on the band, see The Active Set.''In mathematical optimization, a 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 0is called active at x if g_i(x)=0 and inactive at x if g_i(x)>0. Equality constraints are always active. The active set at x is made up of those constraints g_i(x) 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 optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search. ==Active set methods==In general an active set algorithm has the following structure::Find a feasible starting point:repeat until "optimal enough"::''solve'' the equality problem defined by the active set (approximately)::''compute'' the Lagrange multipliers of the active set::''remove'' a subset of the constraints with negative Lagrange multipliers::''search'' for infeasible constraints:end repeatMethods that can be described as active set methods include:* Successive linear programming (SLP) * Sequential quadratic programming (SQP) * Sequential linear-quadratic programming (SLQP) * Reduced gradient method (RG) * Generalized reduced gradient method (GRG) 」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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