论文标题
比较分段符号优化的观点重新制定
Comparing perspective reformulations for piecewise-convex optimization
论文作者
论文摘要
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving, for bounding purposes, piecewise-convex MINLP relaxations obtained by identifying the intervals in which each univariate function is convex or concave and then relaxing the concave parts with精确度提高的分段线性放松。此过程需要引入新的二进制变量，以激活定义函数的间隔。在本文中，我们比较了下边界子问题的三种不同的标准公式，并且在理论上和计算上都表明，与分段线性的情况不同，它们在原始函数的段中可以在段中加强段的配方时，它们并非等效。
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving, for bounding purposes, piecewise-convex MINLP relaxations obtained by identifying the intervals in which each univariate function is convex or concave and then relaxing the concave parts with piecewise-linear relaxations of increasing precision. This process requires the introduction of new binary variables for the activation of the intervals where the functions are defined. In this paper we compare the three different standard formulations for the lower bounding subproblems and we show, both theoretically and computationally, that -- unlike in the piecewise-linear case -- they are not equivalent when the perspective reformulation is applied to reinforce the formulation in the segments where the original functions are convex.
