This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived via using an optimization variable vector, which is called the free vector $\boldsymbol{g}$ by the Theory of Functional Connections. In the spirit of this Theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach.
翻译:本文介绍了一种有效的方法,以解决通过功能连接理论受线性平等制约的二次和非线性编程问题。 这样做时没有使用传统的 Lagrange 倍增效应技术。 更具体地说, 提供了两种截然不同的表达方式( 充分满足平等制约), 以首先解决受限制的二次编程问题, 作为封闭式解决方案的一种不受限制的处理方式。 这些表达方式是通过一个优化可变矢量, 即功能连接理论所谓的自由矢量 $\boldsymbol{g}$ 获得的。 本着这一理论的精神, 对于受平等制约的非线性编程问题, 其解决方案是通过牛顿与优化消除计划相结合的方法获得的。 一致分析得到了拟议方法的数字示例的支持。