[數] 二次規劃
In this paper we present a new algorithm for solving quadratic programming problem (QP) with quadratic constraints.
在本文中，我們提出了一種解帶有二次約束二次規劃問題（QP）的新算法。
The Hybrid Inverse numerical method is a two-step numerical method, comprising of direct matrix inversion and quadratic programming.
混合逆數值算法是一種兩步算法，包含直接矩陣反演求逆和二次規劃兩個步驟。
In the second chapter, we present the basic theory of quadratic programming including conception, optimization al condition and dual problem.
第二章介紹了二次規劃的基礎知識和基本理論，包括基本概念、最優性條件、對偶問題等；
The key problem of training support vector machines is how to solve quadratic programming problem, but for large training examples, the problem is too difficult.
訓練支持向量機的本質問題就是求解二次規劃問題，但對大規模的訓練樣本來說，求解二次規劃問題困難很大。
We present a new branchandbound algorithm for solving quadratic programming problem with quadratic constraints, and analyze the convergence of the algorithm.
提出了一種解帶有二次約束二次規劃問題的新的分枝定界算法對該算法進行了收斂性分析。
According to the standard form of MID system, the problem of mixed integer quadratic programming (MIQP) and its mathematics description can be obtained.
根據混合邏輯動态系統的标準形式，轉化為混合整數二次規劃（MIQP）的問題，同時獲得它的數學描述。
An algorithm of successive quadratic programming(SQP)type is presented to program problems with nonlinear equality and inequality constraints.
建立非線性等式和不等式約束規劃問題的一個序列二次規劃（SQP）型算法。
Some experiments show that the imposed rotation method derived from quadratic programming is a useful method in elastoplastic analysis of reinforced concrete continuous beams.
試驗驗證表明，用二次規劃求解的強迫轉角法是進行鋼筋混凝土連續梁彈塑性分析的有效方法。
A mathematic model of road identification problem is provided and the problem is related with a positive definite quadratic programming problem with inequality constraints.
建立了道路識别問題的數學模型并将上述問題與一個不等式約束的正定二次規劃問題相聯繫。
SVM transforms machine learning to solve an optimization problem, and to solve a convex quadratic programming problem by the optimization theory and method constructing algorithms.
它将機器學習問題轉化為求解最優化問題，并應用最優化理論構造算法來解決凸二次規劃問題。
In this paper a piecewise-linear homotopy algorithm for quadratic programming is developed.
本文發展了一個關于二次規劃問題的分段線性同倫算法。
A new iterative algorithm for quadratic programming is obtained when applying the general algorithm to quadratic programming.
把這種算法應用于二次規劃，得到了二次規劃的一種新的疊代法。
In this paper, penalty parameter for linearly constrained 0-1 quadratic programming is improved.
本文改進了帶線性約束0-1二次規劃問題的罰參數下界。
Based on the fitting results and its inner law, the calculating efficiency in optimizing the reactor is increased via applying the sequential quadratic programming(SQP) method.
基于其内部規律，結合拟合結果，應用序列二次規劃法（SQP）對電抗器進行優化，提高了優化計算效率。
Sequential quadratic programming (SQP) method is an efficient method for solving smooth constrained optimization problems because of its fast convergence rate.
由于序列二次規劃（SQP）算法具有快速收斂速度，所以它是求解光滑約束優化問題的有效方法之一。
Finally, axisymmetrical strain analysis program is work out using FORTRAN90 according to parametric finite element quadratic programming method and some key points about the program are explained.
最後，根據參變量有限元二次規劃算法，用Fortran90 語言編制軸對稱應變分析程式，對程式編制過程中的幾個要點進行說明。
Secondly, the optimal flow distribution scheme in which the quadric multiple regression equation is used as the objective function is determined by the quadratic programming.
以這個二次多元回歸方程為目标函數，用二次規劃方法确定管網的管段流量分配最優方案；
In the first sublevel, the solution of the frictionless unilateral contact problem is obtained by solving an equivalent quadratic programming.
第一層，通過求解與原接觸問題等價的二次規劃問題來進行結構接觸分析；
The theme of this paper is the exploration of algorithm for quadratic programming.
本文的研究主題是二次規劃的算法研究。
A region decomposition method to solve a positive definite quadratic programming is presented.
給出了一個求解正定二次規劃的區域分解方法。
This method splits the primal problem into two parts, a master problem which is a quadratic programming and several sub-problems which are linear programmings.
該方法的高級問題是一個二次規劃問題，而低級子問題是若幹個小規模的線性規劃問題。
To realize weighting in motion, a method for dynamic locally weighting based on sequential quadratic programming was put forward.
為實現動态稱重，提出了基于序列二次規劃的動态可局部稱重方法。
二次規劃（Quadratic Programming, QP）是數學優化中的一個重要分支，屬于非線性規劃的特例。其核心特征在于目标函數為決策變量的二次函數，而約束條件則是這些變量的線性不等式或等式。其标準數學模型可表示為：
$$ begin{align} min{x} quad & frac{1}{2} x^T Q x + c^T x text{s.t.} quad & A{eq} x = b{eq} & A{ineq} x leq b_{ineq} & lb leq x leq ub end{align} $$ 其中：
核心特征與重要性：
典型應用領域：
求解方法： 凸二次規劃（$Q$半正定）有成熟高效的算法：
二次規劃是優化領域的關鍵工具，其特點是二次目标函數和線性約束。當目标函數的二次項矩陣半正定時，問題具有凸性，保證了全局最優解的存在和高效求解的可能性。它在金融、工程控制、機器學習等衆多領域有着廣泛且重要的應用。來源：INFORMS (Institute for Operations Research and the Management Sciences) 相關出版物及資源。
二次規劃（Quadratic Programming，QP）是數學優化中的一個重要分支，主要用于求解目标函數為二次函數、約束條件為線性函數的優化問題。以下是詳細解釋：
二次規劃的标準形式可表示為： $$ begin{aligned} min_{x} quad & frac{1}{2}x^T Q x + c^T x text{s.t.} quad & A x leq b, & C x = d, end{aligned} $$ 其中：
假設需最小化 ( f(x) = x_1 + x_2 )，約束為 ( x_1 + x_2 geq 1 )。
幾何解釋：在直線 ( x_1 + x_2 = 1 ) 上尋找距離原點最近的點，解為 ( x_1 = x_2 = 0.5 )。
quadprog 函數。CVXOPT、SciPy.optimize 庫。二次規劃因其在平衡計算複雜度和實際問題建模中的靈活性，成為工程、金融等領域的核心工具。如需進一步了解具體算法或應用案例，可參考運籌學或優化理論教材。
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