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Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
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 classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently…
We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
We study a class of constrained reinforcement learning (RL) problems in which multiple constraint specifications are not identified before training. It is challenging to identify appropriate constraint specifications due to the undefined…
In realistic production scenarios, Advanced Planning and Scheduling (APS) tools often require manual intervention by production planners, as the system works with incomplete information, resulting in suboptimal schedules. Often, the…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
The daily operation of real-world power systems and their underlying markets relies on the timely solution of the unit commitment problem. However, given its computational complexity, several optimization-based methods have been proposed to…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this…
This paper presents an online path planning algorithm for safe autonomous manipulation of a flexibly constrained object in an unknown environment. Methods for real time identification and characterization of perceived flexible constraints…
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…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…