论文标题
解决有限的优化问题，没有拉格朗日乘数
Solving constrained optimization problems without Lagrange multipliers
论文作者
论文摘要
在许多科学领域，例如热力学，力学，经济学等。这些问题在Lagrange乘数和Lagrangian功能的帮助下进行了限制的优化问题。这些问题是经典解决的。但是，这种方法的缺点是它人为地增加了问题的维度。在这里，我们表明问题的雅各布式的决定因素（要优化和约束的功能）为无效。这个额外的方程将任何等值约束的优化问题转化为相同维度的解决问题。我们还引入了约束矩阵作为约束的雅各布式最大的平方线。约束域的边界由决定因素的无效。约束矩阵还允许编写该函数，以优化其任何变量的泰勒级数，其系数由部分迭代过程确定为代数。
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the disadvantage of this approach is that it artificially increases the dimensionality of the problem. Here, we show that the determinant of the Jacobian of the problem (function to optimize and constraints) is null. This extra equation transforms any equality-constrained optimization problem into a solving problem of same dimension. We also introduced the constraint matrices as the largest square submatrices of the Jacobian of the constraints. The boundaries of the constraint domain are given by the nullity of their determinants. The constraint matrices also permit to write the function to be optimized as a Taylor series of any of its variable, with its coefficients algebraically determined by an iterative process of partial derivation.
