Given the costs and a feasible solution for a finite-dimensional linear program (LP), inverse optimization involves finding new costs that are close to the original and that also render the given solution optimal. Ahuja and Orlin employed the absolute sum norm and the maximum absolute norm to quantify distances between cost vectors, and applied duality to establish that the inverse LP problem can be formulated as another finite-dimensional LP. This was recently extended to semi-infinite LPs, countably infinite LPs, and finite-dimensional conic optimization problems. These works provide sufficient conditions so that the inverse problem also belongs to the same class as the forward problem. This paper extends this result to conic LPs in potentially infinite-dimensional Banach spaces. Moreover, the paper presents concrete derivations for continuous conic LPs, whose special cases include continuous linear programs and continuous conic programs; normed cone programs in Banach spaces, which include second-order cone programs as a special case; and semi-definite programs in Hilbert spaces. These derivations reveal the sharper result that, in each case, the inverse problem belongs to the same specific subclass as the forward problem. Instances where existing forward algorithms can then be adapted to solve the inverse problems are identified. Results in this paper may enable the application of inverse optimization to as yet unexplored areas such as continuous-time economic planning, continuous-time job-shop scheduling, continuous-time network flow, maximum flow with time-varying edge-capacities, and wireless optimization with time-varying coverage requirements.

给定成本和有限维线性程序（LP）的可行解决方案，逆向优化涉及寻找与原始成本接近的新成本，这些新成本还会使给定解决方案达到最佳状态。Ahuja和Orlin使用绝对和范数和最大绝对范数来量化成本向量之间的距离，并应用对偶性建立逆LP问题可以公式化为另一个有限维LP。最近，它扩展到半无限LP，可数无限LP和有限维圆锥优化问题。这些工作提供了充分的条件，因此反问题也与正向问题属于同一类。本文将此结果扩展到潜在无限维Banach空间中的圆锥LP。此外，本文介绍了连续圆锥LP的具体推导，其特殊情况包括连续线性程序和连续圆锥程序。Banach空间中的规范锥程序，其中包括特殊情况下的二阶锥程序；和希尔伯特空间中的半定程序。这些推导揭示了更清晰的结果，在每种情况下，逆问题与正问题属于同一特定子类。然后，可以识别现有正向算法可以适用于解决反问题的实例。本文的结果可能使逆向优化应用于尚未开发的领域，例如连续时间经济计划，连续时间作业车间调度，连续时间网络流量，具有随时间变化的边缘容量的最大流量，