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This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…
This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f + h$…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming…
In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it,…
We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
The main contribution of this thesis is the development of a new algorithm for solving convex quadratic programs. It consists in combining the method of multipliers with an infeasible active-set method. Our approach is iterative. In each…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…