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Recently, there has been significant interest in convex relaxations of the optimal power flow (OPF) problem. A semidefinite programming (SDP) relaxation globally solves many OPF problems. However, there exist practical problems for which…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 2022. In this work, we propose a T-SDP relaxation…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
A recent set of techniques in the robotics community, known as certifiably correct methods, frames robotics problems as polynomial optimization problems (POPs) and applies convex, semidefinite programming (SDP) relaxations to either find or…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
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…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
In this paper, we propose a new nonlinear optimization model to solve semidefinite optimization problems (SDPs), providing some properties related to local optimal solutions. The proposed model is based on another nonlinear optimization…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing global optimality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF)…
A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…
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…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…