Related papers: An efficient Lagrangian-based heuristic to solve a…
Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This…
In this paper, the problem of load uncertainty in compliance problems is addressed where the uncertainty is described in the form of a set of finitely many loading scenarios. Computationally more efficient methods are proposed to exactly…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
Multi-objective optimization aims to solve problems with competing objectives. Evaluating such problems is often slow or expensive, limiting the budget of evaluations. In many applications, historical data from related optimization tasks is…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
Energy storage and demand-side response will play an increasingly important role in the future electricity system. We extend previous results on a single energy storage unit to the management of two energy storage units cooperating for the…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Multi-objective portfolio optimisation is a critical problem researched across various fields of study as it achieves the objective of maximising the expected return while minimising the risk of a given portfolio at the same time. However,…
Sustainable development has emerged as a global priority, and industries are increasingly striving to align their operations with sustainable practices. Parallel machine scheduling (PMS) is a critical aspect of production planning that…
This paper presents a millisecond-level look-ahead control algorithm for energy storage with constant space complexity and worst-case linear run-time complexity. The algorithm connects the optimal control with the Lagrangian multiplier…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
We propose a new splitting and successively solving augmented Lagrangian (SSAL) method for solving an optimization problem with both semicontinuous variables and a cardinality constraint. This optimization problem arises in several contexts…
A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality…
The goal of this paper is to study a multi-objective linear quadratic Gaussian (LQG) control problem. In particular, we consider an optimal control problem minimizing a quadratic cost over a finite time horizon for linear stochastic systems…
This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…
The augmented Lagrange method is employed to address the optimal control problem involving pointwise state constraints in parabolic equations. The strong convergence of the primal variables and the weak convergence of the dual variables are…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…