Related papers: Stochastic Optimization and Coupling
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We characterize the extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Our framework subsumes problems with and without transfers, such as monopoly pricing, principal-optimal bilateral…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Since its inception in the mid-60s, the inventory staggering problem has been explored and exploited in a wide range of application domains, such as production planning, stock control systems, warehousing, and aerospace/defense logistics.…
We present sorting algorithms that represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. A part of the speed advantage is due to the feature to work in-place. Previously, the…
Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad,…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…
We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space S. The main motivation (and result) is that if S in R^d is…
This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…