LiBiT algorithm to solve static pricing problems under mixed multinomial logit demand

Price differentiation is a common strategy for many operators. We study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap.价格差异化是诸多运营商常用的经营策略。本研究针对需求由连续型混合多项对数模型（Continuous Mixed Multinomial Logit）刻画的静态多产品价格优化问题展开探讨。为求解该新型问题，本文设计了一种高效的迭代优化算法，其可渐近收敛至最优解。为此，本文基于信赖域方法构建线性优化（Linear Optimization, LO）问题，以寻得优质可行解并从下界对原问题进行近似。本文还通过分段线性松弛方法构建另一组线性优化问题，从其上界对该优化问题进行近似。随后，本文提出一种新型分支方法以缩小最优性间隙。