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We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…
This paper addresses a novel data science problem, prescriptive price optimization, which derives the optimal price strategy to maximize future profit/revenue on the basis of massive predictive formulas produced by machine learning. The…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…
In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the…
We study a robust selling problem where a seller attempts to sell one item to a buyer but is uncertain about the buyer's valuation distribution. Existing literature shows that robust screening provides a stronger theoretical guarantee than…
In this paper, we explore the challenge of assortment planning in the context of quick-commerce, a rapidly-growing business model that aims to deliver time-sensitive products. In order to achieve quick delivery to satisfy the immediate…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Most sales applications are characterized by competition and limited demand information. For successful pricing strategies, frequent price adjustments as well as anticipation of market dynamics are crucial. Both effects are challenging as…
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by solving convex programs. Finding the worst-case performance of…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…