Related papers: A Duality Result for Robust Optimization with Expe…
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…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…
Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We…
Relying on the co-area formula, an exact relaxation framework for minimizing objectives involving the total variation of a binary valued function (of bounded variation) is presented. The underlying problem class covers many important…
In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…