Related papers: Parabolic optimal control problems with combinator…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
In this paper, we consider a family of simultaneous distributed-boundary optimal control problems ($P_{\alpha}$) on the internal energy and the heat flux for a system governed by a mixed elliptic variational equality with a parameter…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…
We consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
In this paper, we consider a chain of distributed systems governed by a degenerate parabolic equation, which satisfies a weak H\"{o}rmander type condition, with a control distributed over an open subdomain. In particular, we consider two…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the…
Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
This paper considers the linear-quadratic dual control problem where the system parameters need to be identified and the control objective needs to be optimized in the meantime. Contrary to existing works on data-driven linear-quadratic…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…