论文标题
使用不受约束的优化方法来解决简单不可行约束的建模方法
Modeling Approaches for Addressing Simple Unrelaxable Constraints with Unconstrained Optimization Methods
论文作者
论文摘要
我们探讨了用不可行的约束约束解决非线性优化问题的新方法，必须在评估目标函数之前得到满足。我们的方法将不可行的边界约束问题重新制定为不受限制的优化问题，该问题适合现有的无约束优化方法。重新制定依赖于域翘曲来形成优点功能。翘曲的选择决定了可以使用不受约束的问题来找到解决边界约束问题的解决方案的精确度，以及无约束配方（例如平滑度）的关键特性。当域翘曲是一种多输出sigmoidal翘曲时，我们就会发展理论，并且我们探索将不受约束的优化方法应用于公式的实际元素。我们开发了一种利用Sigmoidal翘曲的结构，以确保应用于绩效函数的无约束优化算法将找到所需公差的固定点。
We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. We develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.
