Related papers: The Analysis of Optimization Algorithms, A Dissipa…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…
Optimal control synthesis in stochastic systems with respect to quantitative temporal logic constraints can be formulated as linear programming problems. However, centralized synthesis algorithms do not scale to many practical systems. To…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
Adaptive control provides techniques for adjusting control parameters in real time to maintain system performance despite unknown or changing process parameters. These methods use real data to tune controllers and adjust plant models or…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We consider the distributed optimization problem, where a group of agents work together to optimize a common objective by communicating with neighboring agents and performing local computations. For a given algorithm, we use tools from…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
We develop an optimization framework centered around a core idea: once a (parametric) policy is specified, control authority is transferred to the policy, resulting in an autonomous dynamical system. Thus we should be able to optimize…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…
The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. In this letter we focus on mechanical…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…