Alignment of molecular networks by integer quadratic programming
Alignment of molecular networks by integer quadratic programming
复制标题
通过整数二次规划排列分子网络
DOI：
10.1093/bioinformatics/btm156
复制
发表时间：
2007-07-01
期刊：
影响因子：
5.8
通讯作者：
Chen, Luonan
中科院分区：
文献类型：
--
作者：
Zhenping, Li;Zhang, Shihua;Chen, Luonan
在1984年之前，线性和非线性规划，一个是另一个的子集，在很大程度上沿着沿着不相连的路径发展，甚至没有一个共同的术语。(The使用“编程“来表示“优化“是对这些差异的持续提醒。给定凸分析的一些实际应用，一开始可能令人困惑的是，为什么对它的解的搜索突然以问题本身作为约束优化的形式化陈述而结束。解释是：通常我们不寻求分析解决方案，因为相对较少。（3.5.2，C）如果一个问题可以用凸形式表示，那么存在提供有效数值全局解的计算机程序。[183][423] [424] [422] [367] [353]因此，目标变成了一个给定问题的转化（可能是一个非凸的或组合的问题陈述）到一个等价的凸形式或到一个交替的凸子问题收敛到原来的问题的解决方案：根据凸优化基本定理，凸问题的任何局部最优点（解）都是全局最优的。[63，4.2.2] [324，1]给定凸真实的目标函数g和凸可行集D dom g，这是满足问题约束的所有变量值的集合，我们提出了一个通用的凸优化问题最小化X g（X）服从X ∈ D（685）4.1多项式时间邻域点方法的解的出现[382] [420]。线性规划（凸非线性规划）.
Prior to 1984, linear and nonlinear programming, 4.1 one a subset of the other, had evolved for the most part along unconnected paths, without even a common terminology. (The use of " programming " to mean " optimization " serves as a persistent reminder of these differences.) Given some practical application of convex analysis, it may at first seem puzzling why a search for its solution ends abruptly with a formalized statement of the problem itself as a constrained optimization. The explanation is: typically we do not seek analytical solution because there are relatively few. (3.5.2, C) If a problem can be expressed in convex form, rather, then there exist computer programs providing efficient numerical global solution. [183] [423] [424] [422] [367] [353] The goal, then, becomes conversion of a given problem (perhaps a nonconvex or combinatorial problem statement) to an equivalent convex form or to an alternation of convex subproblems convergent to a solution of the original problem: By the fundamental theorem of Convex Optimization, any locally optimal point (solution) of a convex problem is globally optimal. [63, 4.2.2] [324, 1] Given convex real objective function g and convex feasible set D ⊆ dom g , which is the set of all variable values satisfying the problem constraints, we pose a generic convex optimization problem minimize X g(X) subject to X ∈ D (685) 4.1 nascence of polynomial-time interior-point methods of solution [382] [420]. Linear programming ⊂ (convex ∩ nonlinear) programming.