International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Primal-Dual Active-Set Methods for Convex Quadratic Optimization with Applications

Primal-dual active-set (PDAS) methods are developed for solving quadratic optimization problems (QPs). Such problems arise in their own right in optimal control and statistics–two applications of interest considered in this dissertation–and as subproblems when solving nonlinear optimization problems. PDAS methods are promising as they possess the same favorable properties as other active-set methods, such as their ability to be warm-started and to obtain highly accurate solutions by explicitly identifying sets of constraints that are active at an optimal solution. However, unlike traditional active-set methods, PDAS methods have convergence guarantees despite making rapid changes in active-set estimates, making them well suited for solving large-scale problems.Two PDAS variants are proposed for efficiently solving generally-constrained convex QPs. Both variants ensure global convergence of the iterates by enforcing montonicity in a measure of progress. Besides identifying an estimate set estimate, a novel uncertain set is introduced into the framework in order to house indices of variables that have been identified as being susceptible to cycling. The introduction of the uncertainty set guarantees convergence of the algorithm, and with techniques proposed to keep the set from expanding quickly, the practical performance of the algorithm is shown to be very efficient. Another PDAS variant is proposed for solving certain convex QPs that commonly arise when discretizing optimal control problems. The proposed framework allows inexactness in the subproblem solutions, which can significantly reduce computational cost in large-scale settings. By controlling the level inexactness either by exploiting knowledge of an upper bound of a matrix inverse or by dynamic estimation of such a value, the method achieves convergence guarantees and is shown to outperform a method that employs exact solutions computed by direct factorization techniques.Finally, the application of PDAS techniques for applications in statistics, variants are proposed for solving isotonic regression (IR) and trend filtering (TR) problems. It is shown that PDAS can solve an IR problem with n data points with only O(n) arithmetic operations. Moreover, the method is shown to outperform the state-of-the-art method for solving IR problems, especially when warm-starting is considered. Enhancements to themethod are proposed for solving general TF problems, and numerical results are presented to show that PDAS methods are viable for a broad class of such problems

Irregular grid methods for pricing high-dimensional American options

This thesis proposes and studies numerical methods for pricing high-dimensional American options; important examples being basket options, Bermudan swaptions and real options. Four new methods are presented and analysed, both in terms of their application to various test problems, and in terms of their theoretical stability and convergence properties. A method using matrix roots (Chapter 2) and a method using local consistency conditions (Chapter 4) are found to be stable and to give accurate solutions, in up to ten dimensions for the latter case. A method which uses local quadratic functions to approximate the value function (Chapter 3) is found to be vulnerable to instabilities in two dimensions, and thus not suitable for high-dimensional problems. A proof of convergence related to these methods is provided in Chapter 6. Finally, a method based on interpolation of the value function (Chapter 5) is found to be effective in pricing Bermudan swaptions.

Irregular Grid Methods for Pricing High-Dimensional American Options.

This thesis proposes and studies numerical methods for pricing high-dimensional American options; important examples being basket options, Bermudan swaptions and real options. Four new methods are presented and analysed, both in terms of their application to various test problems, and in terms of their theoretical stability and convergence properties. A method using matrix roots (Chapter 2) and a method using local consistency conditions (Chapter 4) are found to be stable and to give accurate solutions, in up to ten dimensions for the latter case. A method which uses local quadratic functions to approximate the value function (Chapter 3) is found to be vulnerable to instabilities in two dimensions, and thus not suitable for high-dimensional problems. A proof of convergence related to these methods is provided in Chapter 6. Finally, a method based on interpolation of the value function (Chapter 5) is found to be effective in pricing Bermudan swaptions.

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article