On local quasi efficient solutions for nonsmooth vector optimization

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the relationship between local quasi weak efficient solutions and vector critical points

Full Stability In Optimization

The dissertation concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to parametric variational systems including the well-known generalized equations and variational inequalities. Many relationships of full stability with the conventional notions of strong regularity and strong stability are established for a large class of problems of constrained optimization with twice continuously differentiable data. Other applications of full stability to nonlinear programming, to semidefinite programming, and to optimal control problems governed by semilinear elliptic PDEs are also studied

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin

Job shop scheduling with artificial immune systems

The job shop scheduling is complex due to the dynamic environment. When the information of the jobs and machines are pre-defined and no unexpected events occur, the job shop is static. However, the real scheduling environment is always dynamic due to the constantly changing information and different uncertainties. This study discusses this complex job shop scheduling environment, and applies the AIS theory and switching strategy that changes the sequencing approach to the dispatching approach by taking into account the system status to solve this problem. AIS is a biological inspired computational paradigm that simulates the mechanisms of the biological immune system. Therefore, AIS presents appealing features of immune system that make AIS unique from other evolutionary intelligent algorithm, such as self-learning, long-lasting memory, cross reactive response, discrimination of self from non-self, fault tolerance, and strong adaptability to the environment. These features of AIS are successfully used in this study to solve the job shop scheduling problem. When the job shop environment is static, sequencing approach based on the clonal selection theory and immune network theory of AIS is applied. This approach achieves great performance, especially for small size problems in terms of computation time. The feature of long-lasting memory is demonstrated to be able to accelerate the convergence rate of the algorithm and reduce the computation time. When some unexpected events occasionally arrive at the job shop and disrupt the static environment, an extended deterministic dendritic cell algorithm (DCA) based on the DCA theory of AIS is proposed to arrange the rescheduling process to balance the efficiency and stability of the system. When the disturbances continuously occur, such as the continuous jobs arrival, the sequencing approach is changed to the dispatching approach that involves the priority dispatching rules (PDRs). The immune network theory of AIS is applied to propose an idiotypic network model of PDRs to arrange the application of various dispatching rules. The experiments show that the proposed network model presents strong adaptability to the dynamic job shop scheduling environment.postprin

Introduction to Nonsmooth Analysis and Optimization

This book aims to give an introduction to generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for infinite-dimensional nondifferentiable optimization problems that arise in inverse problems, imaging, and PDE-constrained optimization. They cover convex subdifferentials, Fenchel duality, monotone operators and resolvents, Moreau--Yosida regularization as well as Clarke and (briefly) limiting subdifferentials. Both first-order (proximal point and splitting) methods and second-order (semismooth Newton) methods are treated. In addition, differentiation of set-valued mapping is discussed and used for deriving second-order optimality conditions for as well as Lipschitz stability properties of minimizers. The required background from functional analysis and calculus of variations is also briefly summarized.Comment: arXiv admin note: substantial text overlap with arXiv:1708.0418

Bounded Variation in Time

International audienceDescribing a motion consists in defining the state or position $q$ of the investigated system as a function of the real variable $t$, the time. Commonly, $q$ takes its values in some set $Q$, suitably structured for the velocity $u$ to be introduced as the derivative of $t\to q$, when it exists. This, in fact, makes sense if $Q$ is a topological linear space or, more generally, a differential manifold modelled on such a space.For smooth situations, classical dynamics rests, in turn, on the consideration of the acceleration. This is the derivative of $t \to u$, if it exists in the sense of the topological linear structure of $Q$, or, when $Q$ is a manifold, in the sense of some connection. But, from its early stages, classical dynamics has also had to face shocks, i.e. velocity jumps. For isolated shocks, one traditionally resorts to the equations of the dynamics of percussions. Even in the absence of impact, it has been known for a long time that systems submitted to such nonsmooth effects as dry friction may exhibit time discontinuity of the velocity. Furthermore, nonsmooth mechanical constraints may also prevent $t\to u$ from admitting a derivative. In all these cases, the laws governing the motion can no longer be formulated in terms of acceleration

Slope And Geometry In Variational Mathematics

Structure permeates both theory and practice in modern optimization. To make progress, optimizers often presuppose a particular algebraic description of the problem at hand, namely whether the functional components are affine, polynomial, smooth, sparse, etc., and a qualification (transversality) condition guaranteeing the components do not interact wildly. This thesis deals with structure as well, but in an intrinsic and geometric sense, independent of functional representation. On one hand, we emphasize the slope - the fastest instantaneous rate of decrease of a function - as an elegant and powerful tool to study nonsmooth phenomenon. The slope yields a verifiable condition for existence of exact error bounds - a Lipschitz-like dependence of a function's sublevel sets on its values. This relationship, in particular, will be key for the convergence analysis of the method of alternating projections and for the existence theory of steepest descent curves (appropriately defined in absence of differentiability). On the other hand, the slope and the derived concept of subdifferential may be of limited use in general due to various pathologies that may occur. For example, the subdifferential graph may be large (full-dimensional in the ambient space) or the critical value set may be dense in the image space. Such pathologies, however, rarely appear in practice. Semi-algebraic functions - those functions whose graphs are composed of finitely many sets, each defined by finitely many polynomial inequalities - nicely represent concrete functions arising in optimization and are void of such pathologies. To illustrate, we will see that semi-algebraic subdifferential graphs are, in a precise mathematical sense, small. Moreover, using the slope in tandem with semi-algebraic techniques, we significantly strengthen the convergence theory of the method of alternating projections and prove new regularity properties of steepest descent curves in the semi-algebraic setting. To illustrate, under reasonable conditions, bounded steepest descent curves of semi-algebraic functions have finite length and converge to local minimizers - properties that decisively fail in absence of semi-algebraicity. We conclude the thesis with a fresh new look at active sets in optimization from the perspective of representation independence. The underlying idea is extremely simple: around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are "minimal". In the context of standard nonlinear programming, this concept reduces to the active-set philosophy. On the other hand, identifiability is much broader, being independent of functional representation of the problem. This new notion lays a broad and intuitive variational-analytic foundation for optimality conditions, sensitivity, and active-set methods. In the last chapter of the thesis, we illustrate the robustness of the concept in the context of eigenvalue optimization