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An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
While reinforcement learning (RL) holds great potential for decision making in the real world, it suffers from a number of unique difficulties which often need specific consideration. In particular: it is highly non-stationary; suffers from…
We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider…
Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…
This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
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…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
The dynamic portfolio optimization problem in finance frequently requires learning policies that adhere to various constraints, driven by investor preferences and risk. We motivate this problem of finding an allocation policy within a…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…