This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending results from the literature. We introduce the dual robust version of the above problem, prove the Mond-Weir type weak and strong duality theorems, and illustrate with an example.

The quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts that has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy ‘flips’ r binary variables to get a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, very high-quality solutions within a short CPU time.

Water management and soil pollution are hot issues in modern agriculture. While more production of food is required, this quantity has to be obtained using the minimum level of resources and the maximum amortization of assets. Moreover, studies show that in Europe, 30% of water consumption is for agriculture, which has a strong influence not only on the amount of water consumed, but also on its quality due to pollution caused by chemical fertilizers, pesticides and other pollutants used in this sector. Therefore, a major concern is related to the use of water, its efficient consumption, which requires optimal irrigation systems both in terms of water transport and distribution. In this context, but also in the context of a turbid environmental debate, the most important facts in agriculture are the protection of the environment on a long range of time. In order to obtain good results for an irrigation system, in this paper we will present a model for calculating the best suited material for a given geographical area and the optimal water content for irrigation

For the time being, public sector innovation gains new and complex forms of expression: managerial, institutional, technological or communication. This fact is also due to national and international important bodies’ interest for using innovation as resource and tool for public sector development. Characterised by complexity and adaptation, the innovative processes in the public sector embrace the form of medium and long term innovation strategies, holding high key socio-economic impact on the social utility of public sector innovation. The optimality of innovation strategies becomes a tool for improved decisions in public sector management, providing the methodology for their evaluation related to the objectives of development in the public sector.

One of the most effective image processing techniques is the use of convolutional neural networks, where we combine intensity values at grid points in the vicinity of each point. To speed up computations, researchers have developed a dilated version of this technique, in which only some points are processed. It turns out that the most efficient case is when we select points from a sub-grid. In this paper, we explain this empirical efficiency proving that the sub-grid is indeed optimal – in some reasonable sense. To be more precise, we prove that all reasonable optimality criteria, the optimal subset of the original grid is either a sub-grid, or a sub-grid-like set.

In this paper we study a bilinear optimal control problem related to a 2D parabolic-elliptic chemo-repulsion system consider a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a result on the existence of Lagrange multipliers in Banach spaces, we derive an optimality system for a local optimal solution.

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself. Living beings are under the pressures of natural selection, thus are biological flows as well. At the same time, the maintenance of homeostatic conditions, the tenet of physiology, demands regulation of these flows by control of variables. However, due to the very nature of these systems, regulation of flows and control of variables become entangled in closed loops. Therefore, the search for adaptation in flows takes a different path than the search for adaptation in morphological traits. Being at the roots of transfer processes, thermodynamic criteria turn out to be as natural physical candidates. Likewise, being at the roots of physiology, control turns out to be as a natural biological candidate in that path. Here we show how to combine entropy generation, with respect to a generalized process, and control of parameters (in such a generalized process) in order to create a criterium of optimal ways to regulate changes in generalized flows.

This paper proposed a triangular inequality-based rewiring method for the Rapidly exploring Random Tree (RRT)-Connect robot path-planning algorithm that guarantees the planning time compared to the RRT algorithm, to bring it closer to the optimum. To check the proposed algorithm’s performance, this paper compared the RRT and RRT-Connect algorithms in various environments through simulation. From these experimental results, the proposed algorithm shows both quicker planning time and shorter path length than the RRT algorithm and shorter path length than the RRT-Connect algorithm with a similar number of samples and planning time.

What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results suggest a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it.

In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal front, well-distributed, maximally extended and fully filled. Therefore, an effective performance indicator must encompass these features as a whole and must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator, is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto-optimal front. Moreover, DOA computation is easy and fast.

This article investigates robust optimality and duality for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (in short, UNMPVC) via convexificators. Using the properties of convexificators, we introduce generalized standard Abadie constraint qualification (in short, GS-ACQ) for the considered problem UNMPVC. Moreover, we introduce generalized robust version of nonsmooth stationary conditions, namely, weakly stationary point (in short, RW-Stationary), T-stationary point (in short, RT-Stationary), M-stationary point (in short, RM-Stationary) and S-stationary point (in short, RS-Stationary) for UNMPVC. By employing GS-ACQ, we establish that the RS-Stationary is the necessary first-order optimality condition for a local Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNMPVC.

The ratio between blade height and chord, named aspect ratio (AR), plays an important role in compressor aerodynamic design. Once selected, it influences stage performance, blade losses, and the stage stability margin. The choice of the design AR involves both aerodynamic and mechanical considerations, and a reasonable aim is frequently to achieve a desired operating range while maximizing efficiency. For a fixed set of aerodynamic and geometric parameters there will be an optimal choice in AR that achieves a maximum efficiency. However, for a state-of-the-art aero-engine design optimality means multi-objective optimality, that is reaching the highest possible efficiency for a number of operating points while achieving a sufficient stability margin. To this end, the influence of the AR on the performance of the first rotor row of a multistage multi-objective high-speed compressor design is analyzed. A careful setup of the high-speed aerodynamic design problem allows the effect of the AR to be isolated. Close to the optimal AR, only a modest efficiency variation is observed, but a considerable change in compressor stability margin (SM) is noted. Decreasing the AR allows for an increasing efficiency, but at the expense of a reduced surge margin. This allows the designer to trade efficiency for stability. Increasing the AR, however, is shown to reduce both surge margin and efficiency, hence a distinct optimality in stability is observed for the analyzed rotor blade row. In this work, the optimality in surge margin with respect to AR is observed whereas a close to optimal efficiency. The predicted range from AR=1.10 to AR=1.64, is only indicative, considering that the definition of a multi-objective optimality requires balancing efficiency and surge margin and that the choice of balancing these two criteria requires making a design choice along a pareto optimal front.

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. We proposed in this paper to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different climate scenarios compared to the approach using the expected growth and yield. The SAA methods requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality which unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.