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Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…
Given a non-convex optimization problem, we study conditions under which every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is known as KT-invexity and allows to identify the subset of problems where an interior point…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In this paper, the distributed resource allocation optimization problem is investigated. The allocation decisions are made to minimize the sum of all the agents' local objective functions while satisfying both the global network resource…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
We study a problem of fundamental importance to ICNs, namely, minimizing routing costs by jointly optimizing caching and routing decisions over an arbitrary network topology. We consider both source routing and hop-by-hop routing settings.…
Optimizing shared vehicle systems (bike/scooter/car/ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of \emph{complex network externalities} -- changes in the demand/supply at any…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We formulate an economic optimal control problem for transport of natural gas over a large-scale transmission pipeline network under transient flow conditions. The objective is to maximize economic welfare for users of the pipeline system,…
We propose a generalized market equilibrium model using assignment game criteria for evaluating transportation systems that consist of both operators' and users' decisions. The model finds stable pricing, in terms of generalized costs, and…
This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…
This paper develops a highly general convex duality framework for the perturbed utility route choice (PURC) model. We show that the traveler's constrained, potentially non-smooth utility maximization problem admits a dual formulation: an…
Over the past few years, ride-sharing has emerged as an effective way to relieve traffic congestion. A key problem for these platforms is to come up with a revenue-optimal (or GMV-optimal) pricing scheme and an induced vehicle dispatching…
A power market with non-convexities may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, the market players are entitled to receive the uplift payments that…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…
We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…
We introduce a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs. We characterize the time-invariant solutions of a heat equation involving a (weighted) Tarski Laplacian operator, defined for…
Modern communication networks are increasingly equipped with in-network computational capabilities and services. Routing in such networks is significantly more complicated than the traditional routing. A legitimate route for a flow not only…
We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the…
One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…