Related papers: A bilevel optiization based algorithm for solving …
Motivated by the dynamic assortment offerings and item pricings occurring in e-commerce, we study a general problem of allocating finite inventories to heterogeneous customers arriving sequentially. We analyze this problem under the…
In many realistic problems of allocating resources, economy efficiency must be taken into consideration together with social equality, and price rigidities are often made according to some economic and social needs. We study the…
Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…
In this work, we study a generalized Fisher market model that incorporates social influence. In this extended model, a buyer's utility depends not only on their own resource allocation but also on the allocations received by their…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when…
The manufacturing industry is under growing pressure to enhance sustainability while preserving economic competitiveness. As a result, manufacturers have been trying to determine how to integrate onsite renewable energy and real-time…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…
We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed…
Coordination of day-ahead and real-time electricity markets is imperative for cost-effective electricity supply and also to provide efficient incentives for the energy transition. Although stochastic market designs feature the least-cost…
We propose a machine learning method to solve a mean-field game price formation model with common noise. This involves determining the price of a commodity traded among rational agents subject to a market clearing condition imposed by…
We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…
Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…
The relationship between demand and prices of a set of products can be modeled as a linear mapping from logarithmic price changes to logarithmic changes in demand. We consider the problem of estimating the coefficient matrix of this…
Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions…
In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We analyse a general class of bilevel problems, in which the upper-level problem consists in the minimization of a smooth objective function and the lower-level problem is to find the fixed point of a smooth contraction map. This type of…