Implementation of a continuation method for nonlinear complementarity problems via normal maps

Ankara : Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references.In this thesis, a continuation method for nonlinear complementarity problems via normal maps that is developed by Chen, Harker and Pinar [8] is implemented. This continuation method uses the smooth function to approximate the normal map reformulation of nonlinear complementarity problems. The algorithm is implemented and tested with two different plussmoothing functions namely interior point plus-smooth function and piecewise quadratic plus-smoothing function. These two functions are compared. Testing of the algorithm is made with several known problems.Erkan, AliM.S

CLASSIFICATION OF LUNG DISEASE ON X-RAY IMAGES BASED ON GRAY LEVEL CO-OCCURRENCE MATRIX (GLCM) FEATURE EXTRACTION AND BACKPROPAGATION NEURAL NETWORK USING PYTHON GUI

This research aims to develop an automated diagnostic system for classifying lung diseases in X-ray images based on feature extraction using the Gray Level Co-occurrence Matrix (GLCM) with a Backpropagation Artificial Neural Network employing a Python GUI. In this study, 200 lung image data were utilized, divided into four classes with 50 data points each. The four categories of image classes are normal lungs, Pneumonia, Tuberculosis, and Covid-19. The training and testing data were split in a 92:8 ratio, resulting in 184 training data and 16 testing data. The parameters include four input layers, eight hidden layers, two output layers, alpha 0.8, 2000 iteration, and target error = 0.0001. Then, it continued with feature extraction using the GLCM to obtain texture characteristics in lung images. In the training stage, the best results were obtained in iteration 2000 with a Mean Squared Error of 0.005% and a calculated time of 167.319 seconds. At the testing stage, a reasonably high accuracy was obtained, 93.75%, with a calculated time of 0.014 seconds. This result indicates that the method can prove lung images

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

A Fast Smoothing Newton Method for Bilevel Hyperparameter Optimization for SVC with Logistic Loss

Support Vector Classification with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with logistic loss as a bilevel optimization problem in which the upper-level problem and the lower-level problem are both based on logistic loss. The resulting bilevel optimization model is converted to a single-level nonlinear programming (NLP) problem based on the KKT conditions of the lower-level problem. Such NLP contains a set of nonlinear equality constraints and a simple lower bound constraint. The second-order sufficient condition is characterized, which guarantees that the strict local optimizers are obtained. To solve such NLP, we apply the smoothing Newton method proposed in \cite{Liang} to solve the KKT conditions, which contain one pair of complementarity constraints. We show that the smoothing Newton method has a superlinear convergence rate. Extensive numerical results verify the efficiency of the proposed approach and strict local minimizers can be achieved both numerically and theoretically. In particular, compared with other methods, our algorithm can achieve competitive results while consuming less time than other methods.Comment: 27 page

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

Strategic Infrastructure Planning for Autonomous Vehicles

Compared with conventional human-driven vehicles (HVs), AVs have various potential benefits, such as increasing road capacity and lowering vehicular fuel consumption and emissions. Road infrastructure management, adaptation, and upgrade plays a key role in promoting the adoption and benefit realization of AVs.This dissertation investigated several strategic infrastructure planning problems for AVs. First, it studied the potential impact of AVs on the congestion patterns of transportation networks. Second, it investigated the strategic planning problem for a new form of managed lanes for autonomous vehicles, designated as autonomous-vehicle/toll lanes, which are freely accessible to autonomous vehicles while allowing human-driven vehicles to utilize the lanes by paying a toll.This new type of managed lanes has the potential of increasing traffic capacity and fully utilizing the traffic capacity by selling redundant road capacity to HVs. Last, this dissertation studied the strategic infrastructure planning problem for an infrastructure-enabled autonomous driving system. The system combines vehicles and infrastructure in the realization of autonomous driving. Equipped with roadside sensor and control systems, a regular road can be upgraded into an automated road providing autonomous driving service to vehicles. Vehicles only need to carry minimum required on-board devices to enable their autonomous driving on an automated road. The costs of vehicles can thus be significantly reduced

Complementarity and related problems

In this thesis, we present results related to complementarity problems. We study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We present algorithms for this problem, and exemplify it by a numerical example. Following this result, we explore the stochastic version of this linear complementarity problem. Finally, we apply complementarity problems on extended second order cones in a portfolio optimisation problem. In this application, we exploit our theoretical results to find an analytical solution to a new portfolio optimisation model. We also study the spherical quasi-convexity of quadratic functions on spherically self-dual convex sets. We start this study by exploring the characterisations and conditions for the spherical positive orthant. We present several conditions characterising the spherical quasi-convexity of quadratic functions. Then we generalise the conditions to the spherical quasi-convexity on spherically self-dual convex sets. In particular, we highlight the case of spherical second order cones

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor