Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions
研究了参数化半定规划问题中解随参数变化的轨迹几何，发现轨迹上任意点附近仅有六种不同行为，并用例子说明每种行为。
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution trajectory. As our main result, we show that only six distinct behaviors can be observed at a neighborhood of a given point along the solution trajectory. Each possible behavior is then illustrated by an example. Funding: This work was supported by OP RDE [Grant CZ.02.1.01/0.0/0.0/16_019/0000765].