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Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulations remain NP-hard. In this work, we prove that several…

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…

A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…

Water desalination plants (DPs) are among the most critical infrastructures and largest electricity loads in water-scarce regions worldwide. Although reverse osmosis (RO) desalination is the most energy-efficient and dominant technology, it…

In this paper, we study two kinds of singular optimal controls (SOCs for short) problems where the systems governed by forward-backward stochastic differential equations (FBSDEs for short), in which the control has two components: the…

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

Direct Statistical Simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by Direct Numerical Simulation (DNS). That low-order statistics usually…

We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…

We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…

We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…

We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multilinear polynomial problems the optimal values of the continuous…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…

For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization…

Distributed Constraint Satisfaction (DCSP) has long been considered an important problem in multi-agent systems research. This is because many real-world problems can be represented as constraint satisfaction and these problems often…