1,780 research outputs found
OSQP: An Operator Splitting Solver for Quadratic Programs
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
OPTIMIZATION FOR STRUCTURAL EQUATION MODELING: APPLICATIONS TO SUBSTANCE USE DISORDERS
Substance abuse is a serious issue in both modern and traditional societies. Besides health complications such as depression, cancer and HIV, social complications such as loss of concentration, loss of job, and legal problems are among the numerous hazards substance use disorder imposes on societies. Understanding the causes of substance abuse and preventing its negative effects continues to be the focus of much research.
Substance use behaviors, symptoms and signs are usually measured in form of ordinal data, which are often modeled under threshold models in Structural Equation Modeling (SEM). In this dissertation, we have developed a general nonlinear optimizer for the software package OpenMx, which is a SEM package in widespread use in the fields of psychology and genetics. The optimizer solves nonlinearly constrained optimization problems using a Sequential Quadratic Programming (SQP) algorithm. We have tested the performance of our optimizer on ordinal data and compared the results with two other optimizers (implementing SQP algorithm) available in the OpenMx package. While all three optimizers reach the same minimum, our new optimizer is faster than the other two.
We then applied OpenMx with our optimization engine to a very large population-based drug abuse dataset, collected in Sweden from over one million pairs, to investigate the effects of genetic and environmental factors on liability to drug use.
Finally, we investigated the reasons behind better performance of our optimizer by profiling all three optimizers as well as analyzing their memory consumption. We found that objective function evaluation is the most expensive task for all three optimizers, and that our optimizer needs fewer number of calls to this function to find the minimum. In terms of memory consumption, the optimizers use the same amount of memory
Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications
Mixed-integer model predictive control (MI-MPC) can be a powerful tool for
modeling hybrid control systems. In case of a linear-quadratic objective in
combination with linear or piecewise-linear system dynamics and inequality
constraints, MI-MPC needs to solve a mixed-integer quadratic program (MIQP) at
each sampling time step. This paper presents a collection of block-sparse
presolve techniques to efficiently remove decision variables, and to remove or
tighten inequality constraints, tailored to mixed-integer optimal control
problems (MIOCP). In addition, we describe a novel heuristic approach based on
an iterative presolve algorithm to compute a feasible but possibly suboptimal
MIQP solution. We present benchmarking results for a C code implementation of
the proposed BB-ASIPM solver, including a branch-and-bound (B&B) method with
the proposed tailored presolve techniques and an active-set based interior
point method (ASIPM), compared against multiple state-of-the-art MIQP solvers
on a case study of motion planning with obstacle avoidance constraints.
Finally, we demonstrate the computational performance of the BB-ASIPM solver on
the dSPACE Scalexio real-time embedded hardware using a second case study of
stabilization for an underactuated cart-pole with soft contacts.Comment: 27 pages, 7 figures, 2 tables, submitted to journal of Optimal
Control Applications and Method
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