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In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its…
This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that…
The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor…
Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
We propose a novel constrained Bayesian Optimization (BO) algorithm optimizing the design process of Laterally-Diffused Metal-Oxide-Semiconductor (LDMOS) transistors while realizing a target Breakdown Voltage (BV). We convert the…
The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…
This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation.…
In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…