180 research outputs found
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.Dupire equation, parameter identification, optimal control, optimality conditions, SQP method, primal-dual active set strategy
POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots
The present work considers the optimal control of a convective Cahn-Hilliard
system, where the control enters through the velocity in the transport term. We
prove the existence of a solution to the considered optimal control problem.
For an efficient numerical solution, the expensive high-dimensional PDE systems
are replaced by reduced-order models utilizing proper orthogonal decomposition
(POD-ROM). The POD modes are computed from snapshots which are solutions of the
governing equations which are discretized utilizing adaptive finite elements.
The numerical tests show that the use of POD-ROM combined with spatially
adapted snapshots leads to large speedup factors compared with a high-fidelity
finite element optimization
Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming
AbstractThe design of an optimal (output feedback) reduced order control (ROC) law for a dynamic control system is an important example of a difficult and in general non-convex (nonlinear) optimal control problem. In this paper we present a novel numerical strategy to the solution of the ROC design problem if the control system is described by partial differential equations (PDE). The discretization of the ROC problem with PDE constraints leads to a large scale (non-convex) nonlinear semidefinite program (NSDP). For reducing the size of the high dimensional control system, first, we apply a proper orthogonal decomposition (POD) method to the discretized PDE. The POD approach leads to a low dimensional model of the control system. Thereafter, we solve the corresponding small-sized NSDP by a fully iterative interior point constraint trust region (IPCTR) algorithm. IPCTR is designed to take advantage of the special structure of the NSDP. Finally, the solution is a ROC for the low dimensional approximation of the control system. In our numerical examples we demonstrate that the reduced order controller computed from the small scaled problem can be used to control the large scale approximation of the PDE system
Model order reduction approaches for infinite horizon optimal control problems via the HJB equation
We investigate feedback control for infinite horizon optimal control problems
for partial differential equations. The method is based on the coupling between
Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is
well-known that HJB equations suffer the so called curse of dimensionality and,
therefore, a reduction of the dimension of the system is mandatory. In this
report we focus on the infinite horizon optimal control problem with quadratic
cost functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati
equation based approach. Finally, we present numerical examples and discuss
several features of the different methods analyzing advantages and
disadvantages of the reduction methods
The ACS Exams Institute Undergraduate Chemistry Anchoring Concepts Content Map I: General Chemistry
To provide tools for programmatic assessment related to the use of ACS Exams in undergraduate chemistry courses, the ACS Exams Institute has built a content map that applies to the entire undergraduate curriculum. At the top two levels, the grain size of the content classification is large and spans the entire undergraduate curriculum. At the bottom two levels, the grain size of the content is more fine and tuned to specific course levels of the curriculum. This paper presents all four levels of the map as identified for first-year general chemistry
Order reduction approaches for the algebraic Riccati equation and the LQR problem
We explore order reduction techniques for solving the algebraic Riccati
equation (ARE), and investigating the numerical solution of the
linear-quadratic regulator problem (LQR). A classical approach is to build a
surrogate low dimensional model of the dynamical system, for instance by means
of balanced truncation, and then solve the corresponding ARE. Alternatively,
iterative methods can be used to directly solve the ARE and use its approximate
solution to estimate quantities associated with the LQR. We propose a class of
Petrov-Galerkin strategies that simultaneously reduce the dynamical system
while approximately solving the ARE by projection. This methodology
significantly generalizes a recently developed Galerkin method by using a pair
of projection spaces, as it is often done in model order reduction of dynamical
systems. Numerical experiments illustrate the advantages of the new class of
methods over classical approaches when dealing with large matrices
Enhanced antiviral function of magnesium chloride-modified Heparin on a broad spectrum of viruses
Previous studies reported on the broad-spectrum antiviral function of heparin. Here we investigated the antiviral function of magnesium-modified heparin and found that modified heparin displayed a significantly enhanced antiviral function against human adenovirus (HAdV) in immortalized and primary cells. Nuclear magnetic resonance analyses revealed a conformational change of heparin when complexed with magnesium. To broadly explore this discovery, we tested the antiviral function of modified heparin against herpes simplex virus type 1 (HSV-1) and found that the replication of HSV-1 was even further decreased compared to aciclovir. Moreover, we investigated the antiviral effect against the new severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) and measured a 55-fold decreased viral load in the supernatant of infected cells associated with a 38-fold decrease in virus growth. The advantage of our modified heparin is an increased antiviral effect compared to regular heparin
Sexual harassment and abuse in sport: The research context
This special issue of the Journal of Sexual Aggression draws on the contributions to a Symposium on âSexual Harassment in Sport â Challenges for Sport Psychology in the New Millenniumâ, held at the Xth Congress of the International Society for Sport Psychology, Skiathos, Greece from May 28th to June 2nd 2001. The symposium, which was organised by the authors of this editorial, was intended to move forward the international research agenda on sexual harassment and abuse in sport and to examine professional practice issues for sport psychologists. It was clear from the attendance of over 60 delegates at that symposium that international interest in this subject is growing. Further evidence of this came from the attendance of 26 members states â from Azerbaijan to Sweden - at a Council of Europe seminar on The Protection of Children, Young People and Women in Sport, held in Helsinki in September 2001
Life cycle assessment of Polychlorinated Biphenyl contaminated soil remediation processes
Goal and scope. A life-cycle assessment (LCA) was performed to evaluate the environmental impacts of the remediation of industrial soils contaminated by polychlorobiphenyl (PCB). Two new bioremediation treatment options were compared with the usual incineration process. In this attributional LCA, only secondary impacts were considered. The contaminated soil used for the experiments contained 200 mg of PCB per kg. Methods. Three off-site treatments scenarios were studied: 1) bioremediation with mechanical aeration, 2) bioremediation with electric aeration and 3) incineration with natural gas. Bioremediation processes were designed from lab-scale, scale-up and pilot experiments. The incineration technique was inspired by a French plant. A semi-quantitative uncertainty analysis was performed on the data. Environmental impacts were evaluated with the CML 2001 method using the Simapro software program. Results and discussion. In most compared categories, the bioremediation processes are favorable. Of the bioremediation options, the lowest environmental footprint was observed for electric aeration. The uncertainty analysis supported the results that compared incineration and bioremediation but decreased the difference between the options of aeration. The distance of transportation was one of the most sensitive parameters, especially for bioremediation. At equal distances between the polluted sites and the treatment plant, bioremediation had fewer impacts than incineration in eight out of thirteen categories. Conclusions. The use of natural gas for the incineration process generated the most impacts. Irrespective of the aeration option, bioremediation was better than incineration. Recommendations. The time of treatment should be taken into account. More precise and detailed data are required for the incineration scenario. More parameters of biological treatments should be measured. LCA results should be completed using ecological and health risk assessment and an acceptability evaluation
- âŠ