Related papers: Optimality Conditions for Convex Stochastic Optimi…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…

We formulate bang-bang, purification, and minimization principles in dual Banach spaces with Gelfand integrals and provide a complete characterization of the saturation property of finite measure spaces. We also present a new application of…

The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators are considered. Under some regularity condition assumed for the solution, the rate of convergence of implicit Euler approximations is…

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

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 develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functionals, we introduce closed convex processes -- set-valued…

The main problem considered in the present paper is to single out classes of convex sets, whose convexity property is preserved under nonlinear smooth transformations. Extending an approach due to B.T. Polyak, the present study focusses on…

Integrated learning and optimization (ILO) is a framework in contextual optimization which aims to train a predictive model for the probability distribution of the underlying problem data uncertainty, with the goal of enhancing the quality…

Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…

This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…

We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…

We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…