Related papers: Convex duality for stochastic singular control pro…
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in…
In this paper, an open problem is solved, for the stochastic optimal control problem with delay where the control domain is nonconvex and the diffusion term contains both control and its delayed term. Inspired by previous results by \O…
This paper studies convex problems of Bolza in the conjugate duality framework of Rockafellar. We parameterize the problem by a general Borel measure which has direct economic interpretation in problems of financial economics. We derive a…
Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial…
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the…
We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…
This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several…
We address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and…
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg…
Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provides valuable analytical insights and new proofs of classical…
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…
We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas-Rachford (DR) algorithm. We obtain an expression for the fixed point of…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
The paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem where the probability of failure to satisfy given state constraints is explicitly bounded. We leverage the notion of exit…
This paper studies Merton's problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a tracking formulation where the fund manager aims to maximize the trade-off between the expected…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…
The main theme of this thesis is the development of computational methods for classes of infinite-dimensional optimization problems arising in optimal control and information theory. The first part of the thesis is concerned with the…