Inclusion Constraints Research Articles

Mathematical programming with multiple sets split monotone variational inclusion constraints

Abstract In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two numerical examples are given to demonstrate our results. As applications of our convergence theorem of the hierarchical problem, we study the unique solution for the following problems: mathematical programming with multiply sets split variational inclusion and fixed point set constraints; mathematical programming with multiple sets split variational inequalities and fixed point set constraints; the variational inequality problem with a system of mixed type equilibria and fixed point set constraints; the variational inequality problem with multiple sets split system of mixed type equilibria and fixed point set constraints; mathematical programming with a system of mixed type equilibria and fixed point set constraints. We give iteration processes for these types of problems and establish the strong convergence for the unique solution of these problems. For our special case, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibria problem; the minimum norm solution of the system of mixed type equilibria problem. Our results will have many applications in diverse fields of science.

Grouping and Sequencing of Machining Operations for High Volume Transfer Lines

Transfer lines are costly assets used for manufacturing of voluminous quantities of a dedicated discrete product following a pre- defined process plan. This paper deals with the problem of optimal grouping, sequencing and utilization of the dedicated machinery that goes into such transfer lines. A time objective function has been utilized. Handling time, which is an important component of cycle time, is assumed to be comprised of tool change time, time required to reposition and transport the workpiece and refixturing & reloading time. A new mixed integer linear programming model is developed to solve the problem with the aforementioned objectives while respecting a set of constraints, which include machine loading, tool allocation, tool magazine limit, takt time limit and precedence & inclusion constraints. A numerical case study is utilized to illustrate the functionality of the model.

Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints

We introduce and analyze a hybrid iterative algorithm by combining Korpelevich's extragradient method, the hybrid steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of finitely many nonexpansive mappings, the solution set of a generalized mixed equilibrium problem (GMEP), the solution set of finitely many variational inclusions, and the solution set of a convex minimization problem (CMP), which is also a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solving a hierarchical variational inequality problem with constraints of the GMEP, the CMP, and finitely many variational inclusions.

Balancing reconfigurable machining lines via a set partitioning model

We consider the problem of constructing an optimal machining line as a sequence of workstations performing specific sets of operations. The line is required to satisfy the given precedence order on operations, inclusion, exclusion and accessibility constraints. The cycle times of workstations are computed taking into account the processing and sequence dependent set-up times of operations and must not exceed the given bound. For solving the problem, we propose a reduction of this machining line design problem to a set partitioning type problem. This approach implies generating all possible workstations and, for each workstation, solving a scheduling problem in order to find the sequence of operations which minimises the total set-up time. To do this, a dynamic programming algorithm is developed. Several preprocessing procedures are suggested to reduce the number of workstations. A set of exact algorithms are proposed to solve the obtained set partitioning type problem: a constraint generation, a branch and cut, and a parallel branch and cut algorithms. Our experimental investigation demonstrated that the proposed method achieves a significant improvement in CPU times over those required by a previous study that is based on a different model formulation, and also, that the proposed method is able to solve large-sized problem instances.

A technique for extracting behavioral sequence patterns from GPS recorded data

The mobile wireless market has been attracting many customers. Technically, the paradigm of anytime-anywhere connectivity raises previously unthinkable challenges, including the management of million of mobile customers, their profiles, the profiles-based selective information dissemination, and server-side computing infrastructure design issues to support such a large pool of users automatically and intelligently. In this paper, we propose a data mining technique for discovering frequent behavioral patterns from a collection of trajectories gathered by Global Positioning System. Although the search space for spatiotemporal knowledge is extremely challenging, imposing spatial and temporal constraints on spatiotemporal sequences makes the computation feasible. Specifically, the mined patterns are incorporated with synthetic constraints, namely spatiotemporal sequence length restriction, minimum and maximum timing gap between events, time window of occurrence of the whole pattern, inclusion or exclusion event constraints, and frequent movement patterns predictive of one ore more classes. The algorithm for mining all frequent constrained patterns is named cAllMOP. Moreover, to control the density of pattern regions a clustering algorithm is exploited. The proposed method is efficient and scalable. Its efficiency is better than that of the previous algorithms AllMOP and GSP with respect to the compactness of discovered knowledge, execution time, and memory requirement.

Mann-Type Extragradient Methods for General Systems of Variational Inequalities with Multivalued Variational Inclusion Constraints in Banach Spaces

We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich’s extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

Optimality conditions of strict minimality in optimization problems under inclusion constraints

In this paper, we extend the concepts of linearizing cone, regularity assumption and Lagrange multiplier rule due to Maurer and Zowe [H. Maurer, J. Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Program. 16 (1979) 98–110] to an optimization problem under inclusion constraints. By virtue of the Robinson–Ursescu open mapping theorem, we obtain a Kuhn–Tucker necessary optimality condition. Moreover, we propose a Lagrangian by using the support function for set-valued maps, and establish some second-order sufficient and necessary optimality conditions for a strict local minimizer of order 2 based on the second-order derivative of the Lagrangian. As applications, we also investigate some second-order optimality conditions for the strict local minimizer of order 2 of a smooth scalar optimization problem with equality and inequality constraints.

Spectral optimization problems with internal constraint

We consider spectral optimization problems with internal inclusion constraints, of the formmin{λk(Ω):D⊂Ω⊂Rd,|Ω|=m}, where the set D is fixed, possibly unbounded, and λk is the k-th eigenvalue of the Dirichlet Laplacian on Ω. We analyze the existence of a solution and its qualitative properties, and rise some open questions.

Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization

In this paper, we propose several second-order derivatives for set-valued maps and discuss their properties. By using these derivatives, we obtain second-order necessary optimality conditions for strict efficiency of a set-valued optimization problem with inclusion constraints in real normed spaces. We also establish second-order sufficient optimality conditions for strict efficiency of the set-valued optimization problem in finite-dimensional normed spaces. As applications, we investigate second-order sufficient and necessary optimality conditions for a strict local efficient solution of order two of a nonsmooth vector optimization problem with an abstract set and a functional constraint.

Mineralogy, fluid inclusion, and oxygen isotope constraints on the genesis of the Lalla Zahra W-(Cu) deposit, Alouana district, northeastern Morocco

The Lalla Zahra W-(Cu) prospect of northeastern Morocco is hosted in a Devonian volcaniclastic and metasedimentary sequence composed of graywacke, siltstone, pelite, and shale interlayered with minor tuff and mudstone. Intrusion of the 284 ± 7 Ma Alouana concentrically zoned, two micas, calc-alkaline, and post-collisional Alouana granitoid pluton has contact metamorphosed the host rocks, giving rise to a metamorphic assemblage of quartz, plagioclase, biotite, muscovite, chlorite, and alusite, and cordierite. The mineralization occurs in and along subvertical, 20 to 40 cm thick, and structurally controlled tensional veins composed of quartz accompanied by molybdenite, wolframite, scheelite, base metal sulphides, carbonates, barite, and fluorite. Three main stages of mineralization (I, II, and III), each characterized by a specific mineral assemblage and/or texture, are recognized. Quartz dominates in all the veins and commonly displays multiple stages of vein filling and brecciation, and a variety of textures. The early tungsten-bearing stage consists of quartz-1, tourmaline, muscovite, wolframite, scheelite, and molybdenite. With advancing paragenetic sequence, the mineralogy of the veins shifted from stage I tungsten-bearing mineralization through stage II, dominated by base metal sulphides, to stage III with late barren carbonates and barite ± fluorite mineral assemblages. Pervasive hydrothermal alteration affected, to varying degrees, the Alouana intrusion, resulting in microclinization, albitization, episyenitization, and greisenization of all the granitic units. Fluid inclusion data yield homogenization temperatures ranging from 124°C to 447°C for calculated salinity estimates in the range of 0.4 to ~60 wt% NaCl equiv. Similarly, the δ18O values for the three generations of quartz range from 11.7‰ to 13.9‰ V-SMOW. Calculated δ18O values of the parent fluid in the range between −3‰ and +9‰ V-SMOW are consistent either with a mixture of water of different origins, including magmatic water, or an origin from seawater or meteoric water that probably exchanged oxygen with rocks at elevated temperatures. The coexistence of CO2-rich and H2O-rich fluid inclusions reflect the presence of a boiling fluid associated with the deposition of the early tungsten-bearing stage mineralization at relatively high temperature. The general temperature and salinity decrease with advancing paragenetic sequence suggest that the early high temperature, magmatic, highly saline, and boiling fluid mixed with meteoric non-boiling fluid results in the precipitation of base metal sulphide and carbonate–barite stage mineral assemblages, respectively.

Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints

In this paper, we are concerned with a set-valued fractional extremal programming problem under inclusion constraints. Our approach consists of using the extremal principle (an approach initiated by Mordukhovich, which does not involve any convex approximations and convex separation arguments) for the study of necessary optimality conditions.

A Necessary Condition for Optimality in Multi Objective Programming under Inclusion Constraints

Optimality conditions for multi objective programming problems have been studied extensively in the literature. A necessary condition for Pareto optimality is derived by reducing the multi objective programming under inclusion constraints to systems of single objective problem and then using known results of them. The result is reasonable and efficient. Our aim in this paper is to get the optimality condition of problem (MOP) by a lemma which helps reducing multi objective optimality problem to systems of single objective ones.

New systems of generalized quasi-variational inclusions in FC-spaces and applications

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure. By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

Second-order optimality conditions using approximations for nonsmooth vector optimization problems under inclusion constraints

Second-order necessary conditions and sufficient conditions for optimality in nonsmooth vector optimization problems with inclusion constraints are established. We use approximations as generalized derivatives and avoid even continuity assumptions. Convexity conditions are not imposed explicitly. Not all approximations in use are required to be bounded. The results improve or include several recent existing ones. Examples are provided to show that our theorems are easily applied in situations where several known results do not work.

Second-order conditions for nonsmooth multiobjective optimization problems with inclusion constraints

This paper investigates second-order optimality conditions for general multiobjective optimization problems with constraint set-valued mappings and an arbitrary constraint set in Banach spaces. Without differentiability nor convexity on the data and with a metric regularity assumption the second-order necessary conditions for weakly efficient solutions are given in the primal form. Under some additional assumptions and with the help of Robinson -Ursescu open mapping theorem we obtain dual second-order necessary optimality conditions in terms of Lagrange-Kuhn-Tucker multipliers. Also, the second-order sufficient conditions are established whenever the decision space is finite dimensional. To this aim, we use the second-order projective derivatives associated to the second-order projective tangent sets to the graphs introduced by Penot. From the results obtained in this paper, we deduce and extend, in the special case some known results in scalar optimization and improve substantially the few results known in vector case.

Fuzzy Robust Credibility-Constrained Programming for Environmental Management and Planning

In this study, a fuzzy robust credibility-constrained programming (FRCCP) is developed and applied to the planning for waste management systems. It incorporates the concepts of credibility-based chance-constrained programming and robust programming within an optimization framework. The developed method can reflect uncertainties presented as possibility-density by fuzzy-membership functions. Fuzzy credibility constraints are transformed to the crisp equivalents with different credibility levels, and ordinary fuzzy inclusion constraints are determined by their robust deterministic constraints by setting α-cut levels. The FRCCP method can provide different system costs under different credibility levels (λ). From the results of sensitivity analyses, the operation cost of the landfill is a critical parameter. For the management, any factors that would induce cost fluctuation during landfilling operation would deserve serious observation and analysis. By FRCCP, useful solutions can be obtained to provide decision-making support for long-term planning of solid waste management systems. It could be further enhanced through incorporating methods of inexact analysis into its framework. It can also be applied to other environmental management problems.

A Review of Fluid Inclusion Constraints on Mineralization in the Irish Ore Field and Implications for the Genesis of Sediment-Hosted Zn-Pb Deposits

Many fluid inclusion studies have been carried out in the Irish Midlands basin ore field (Lower Carboniferous) since the earliest work by Ed Roedder in the late 1960s. Results show that, in the ore deposits, the total range in fluid salinity is 4 to 28 wt percent NaCl equiv but with the majority billing in the moderate-salinity range between 8 and 19 wt percent. This variability is interpreted in terms of mixing between moderate-salinity ore fluids and low-temperature brines during ore formation. The most northerly ore deposits of Navan and Abbey-town are, distinct in containing fluids of both lower and higher salinity than is typical of the Waulsortian-hosted deposits farther south (Tynagh, Silvermines, Lisheen, and Galmoy). Subeconomic prospects tend to display a narrower range, in salinity mostly at the lower end of the range observed in the ore deposits. In some prospects, and cm the margins of some ore deposits, evidence for dilution is observed, interpreted to reflect mixing between hydrothermal fluids and unmodified seawater. This process is inferred to be unfavorable for mineralization.Homogenization temperatures, a reasonable proxy for true trapping temperatures in the ore field, range from 70 degrees to 280 degrees C but with the majority falling between 130 degrees and 240 degrees C. There is no evidence for systematic stretching or leakage of inclusions related to the postentrapment heating implied by elevated thermal maturity indicators. The highest temperatures are observed in the Waulsortian-hosted systems, with peak temperatures of -280 degrees C supported by local, high-grade Cu and Ni mineralization. in the Navan and Abbeytown deposits, lower temperature fluids appear to have been more prevalent. The subeconomic prospects formed over essentially the same temperature range as the ore deposits (90 degrees-270 degrees C), with the exception of the morphologically and texturally distinct Mississippi Valley-type (MVT) systems in the region (e.g. Kinnitty, Harberton Bridge) that formed at lower temperatures (50 degrees-100 degrees C).Similar hydrothermal fluids to those recorded in both deposits and prospects are widely observed in dolomite (and sometimes calcite) cements within Courceyan-Arundian-age rocks, indicating that hydrothermal fluid activity occurred over an extremely large area (>30,000 km(2)) and probably over an extended time period. There is a broad regional division in fluid properties, suggesting that the northwestern and southeastern provinces, separated by the trace of the Iapetus suture zone, may represent partly decoupled, large-scale flow regimes. Up to three, low-temperature brine types are also recorded by cements in the host-rock sequence, indicating that a complex range of evaporation and fluid-rock interaction processes were ongoing in the shallow basin succession during the period of hydrothermal activity.Halogen data show that fluids involved in mineralization were originally seawater-derived brines, produced by evaporation to varying degrees. Relatively high temperature, basement-interacted hydrothermal fluids were derived from partially evaporated seawater (molar Cl/Br = 559-825). Their compositions can be explained by dolomitization in the Carboniferous succession prior to circulation to depth; alkali exchange, reduction, and metal-leaching from the lower Paleozoic basement; and mixing with low-temperature brines that locally penetrated the upper parts of the basement rock package. Fertile ore fluids appear to be characterized by higher delta O-18 (+7 to +9 parts per thousand), lower delta D (-25 to -45 parts per thousand) and much higher metal contents than otherwise similar fluids sampled in basement-hosted feeder veins distal to deposits. This may reflect highly efficient metal scavenging in deeper and/or higher temperature reaction zones that underlie the principal deposits. In the ore deposits, these fluids mixed with Br-enriched bittern brines (Cl/Br similar to 290) produced by evaporation of Carboniferous seawater past halite saturation. It is inferred that bittern brine generation occurred in the shallow marine shelf regions in the footwalls to the synsedimentary fault systems that controlled the localization of mineralization. These brines then migrated into hanging-wall depressions where they ponded within permeable sediments and became enriched in H2S via bacteriogenic sulfate reduction. The coincidence of structurally controlled, high-temperature reaction zones, brine-producing footwalls, and hanging-wall traps, with bacterial blooms above upwelling plumes of hydrothermal fluids, can be interpreted as a self-organizing system that locally converged on ore-forming conditions. Understanding the first-order structural control of the ore systems will therefore be critical for predicting new deposits.The Irish ore field presents arguably the best database available on the thermal and chemical characteristics of hydrothermal fluids involved in sediment-hosted ore genesis. The system shares much of the variety and complexity observed in other intracratonic basin-hosted Zn-Pb(Ba) ore districts. This includes the coexistence of contrasting styles of mineralization that are typically observed in the more distal and platform-marginal parts of the basinal environment. The thermal and chemical fluid heterogeneity observed is typical of modern intracratonic basin systems and should be expected in large paleohydrothermal systems where recharge of surface-derived fluids is involved.

Fluid Inclusion Constraints on the Genesis of Gold in the Darasun District (Eastern Transbaikalia), Russia

Fluid Inclusion Constraints on the Genesis of Gold in the Darasun District (Eastern Transbaikalia), Russia

Balancing lines with CNC machines: A multi-start ant based heuristic

We are working on a machining line balancing problem involving specific constraints. The studied lines are paced and serial, i.e. a part to be machined passes through a sequence of stations. The stations are equipped with CNC (Computer Numerical Control) machines. A CNC machine is a mono-spindle head machine which can use sequentially different tools and can rotate the part in order to perform different tasks. Such a machine is guided by a computer numerical controller system. As usual with machining lines, this problem is subject to precedence constraints as well as exclusion and inclusion constraints. Moreover, the station workload depends on the sequence in which the tasks are assigned because of set-up times related to the change and displacement of tools, rotation of the part, etc. In addition, accessibility constraints have to be considered. Two types of CNC machines with different characteristics can be used. Several tasks require a particular type of machine. The objective is to assign a given set of tasks, required for part machining, as well as a given set of machines to a sequence of stations while minimizing the total cost of the line. In this paper, a multi-start heuristic is proposed and tested on real life industrial problems.

Two-variable logic on data trees and XML reasoning

Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result, decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.