Related papers: De-risking solutions to optimization problems
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating…
The application of combinatorial optimization problems to solving the problems of planning processes for industries based on a fund of reconfigurable production resources is considered. The results of their solution by mixed integer…
This paper considers an empirical risk minimization problem under heavy-tailed settings, where data does not have finite variance, but only has $p$-th moment with $p \in (1,2)$. Instead of using estimation procedure based on truncated…
In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…
We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
An optimization of caching strategies is proposed as a formal approach allowing us a more efficient use of two-level computer memory. This approach is based on a set of mathematical models and a set of theorems, permitting analytical…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…