We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix at almost every iteration. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. It can be configured to be division-free once an initial matrix factorization is carried out, making it suitable for real-time applications in embedded systems. In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The method also supports factorization caching and warm starting, making it particularly efficient

We present a general purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix at almost every iteration. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. It can be configured to be division-free once an initial matrix factorization is carried out, making it suitable for real-time applications in embedded systems. In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The method also supports factorization caching and warm starting, making it particularly efficient when solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint, is library-free, and has been extensively tested on many problem instances from a wide variety of application areas. It is typically ten times faster than competing interior point methods, and sometimes much more when factorization caching or warm start is used. OSQP has already shown a large impact with tens of thousands of users both in academia and in large corporations.

The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well-known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive information regarding problem infeasibility for optimization problems with linear or quadratic objective functions and conic constraints, which includes quadratic, second-order cone, and semidefinite programs. In particular, we show that in the limit the iterates either satisfy a set of first-order optimality conditions or produce a certificate of either primal or dual infeasibility. Based on these results, we propose termination criteria for detecting primal and dual infeasibility.

SUMMARY – Premature infants are susceptible to oxidative stress that causes neonatal disease such as retinopathy of prematurity (ROP). Oxidative stress is an imbalance between the production of pro-oxidants and the ability of the body to detoxify their harmful effects by antioxidants. The proliferative phase 2 ROP occurs at around 33 rd postmenstrual week (pmw). The purpose of our study was to evaluate the pro-oxidant/antioxidant status in preterm infants at 33 rd pmw. The study included 59 premature infants. ROP was classified according to the International Classification of Retinopathy of Prematurity. Total oxidative status (TOS), total antioxidant status (TAS), malondialdehyde (MDA) and paraoxonase 1 (PON1) activity were determined spectrophotometrically. The values of the pro-oxidants TOS and MDA were significantly higher in infants with ROP as compared to infants without ROP (p<0.05 both). There were no significant differences in the values of TAS and PON1 between the infants with and without ROP. According to study results, TOS and MDA are good markers of oxidative stress, whereas TAS and PON1 activity are unreliable in assessing antioxidant protection.

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