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First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
In this paper we propose a framework to analyze iterative first-order optimization algorithms for time-varying convex optimization. We assume that the temporal variability is caused by a time-varying parameter entering the objective, which…
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…
In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…
Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and…
Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…
Quantum computing promises exponential acceleration for fluid flow simulations, yet the measurement overhead required to extract flow features from quantum-encoded flow field data fundamentally undermines this advantage--a critical…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…
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…
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…
The optimal power flow (OPF) is an optimization model dedicated to the development of computational tools used for the planning and operation of electric power systems (EPS). In this work, based on the polar formulation, an extended convex…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…