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In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as n-polynomial exponential type s-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications. [ABSTRACT FROM AUTHOR]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

Abstract This paper proposes a novel decomposition method based on user-preference and developed a variation of the decomposition based multi-objective optimization algorithm (MOEA/D) targeting only solutions in a small region of the Pareto-front defined by the preference information supplied by the decision maker (DM). This is particularly advantageous for solving multi-objective optimization problems (MOPs) with more than 3 objectives, i.e., many-objective optimization problems (MaOPs). As the number of objectives increases, the ability of an EMO algorithm to approximate the entire Pareto front (PF) is rapidly diminishing. In this paper, we first propose a novel scalarizing function making use of a series of new reference points derived from a reference point specified by the DM in the preference model. Based on this scalarizing function, we then develop a user-preference-based EMO algorithm, namely R-MOEA/D. One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point, which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms. Our experimental results on multi-objective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region, resulting in competitive performances. In an interactive setting when the DM changes the reference point during optimization, R-MOEA/D has a faster response speed and performance than the compared algorithms, showing its robustness and adaptability to changes of the preference model. Furthermore, the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush-Kuhn-Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established. [ABSTRACT FROM AUTHOR]

A chance constrained optimization problem over a finite distribution involves a set of scenario constraints from which a small subset can be violated. We consider the setting where all scenario constraints are mixed-integer convex. Existing works typically consider a mixed integer nonlinear programming (MINLP) formulation of this problem by introducing binary variables to indicate which constraint systems are to be satisfied or violated. A variety of cutting plane approaches for this MINLP formulation have been developed. In this paper we consider a family of cuts in the original space rather than those in the extended space of the MINLP reformulation. These cuts, known as quantile cuts, can be viewed as a projection of the well known family of mixing inequalities for the MINLP reformulation onto the original problem space. We show that the closure of the infinite family of all quantile cuts has a finite description. An important corollary of this result is that for linear chance constrained problems the quantile closure is polyhedral. We further show that a recursive application of quantile closure operations recovers the convex hull of the nonconvex chance constrained set in the limit, and in the pure integer setting the convergence is finite. We show that separation of quantile cuts is in general NP-hard, develop a heuristic separation method, and demonstrate its effectiveness through a computational study. We also study an approximation of the quantile closure and propose a generalization by grouping scenarios. [ABSTRACT FROM AUTHOR]

The zero propellant maneuver (ZPM) is an advanced space station, large angle attitude maneuver technique, using only control momentum gyroscopes (CMGs). Path planning is the key to success, and this paper studies the associated multi-objective optimization problem. Three types of maneuver optimal control problem are formulated: (i) momentum-optimal, (ii) time-optimal, and (iii) energy-optimal. A sensitivity analysis approach is used to study the Pareto optimal front and allows the tradeoffs between the performance indices to be investigated. For example, it is proved that the minimum peak momentum decreases as the maneuver time increases, and the minimum maneuver energy decreases if a larger momentum is available from the CMGs. The analysis is verified and complemented by the numerical computations. Among the three types of ZPM paths, the momentum-optimal solution and the time-optimal solution generally possess the same structure, and they are singular. The energy-optimal solution saves significant energy, while generally maintaining a smooth control profile. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. [ABSTRACT FROM AUTHOR]

In this paper, optimality conditions are presented and analyzed for the cardinality-constrained cone programming arising from finance, statistical regression, signal processing, etc. By introducing a restricted form of (strict) Robinson constraint qualification, the first-order optimality conditions for the cardinality-constrained cone programming are established based upon the properties of the normal cone. After characterizing further the second-order tangent set to the cardinality-constrained system, the second-order optimality conditions are also presented under some mild conditions. These proposed optimality conditions, to some extent, enrich the optimization theory for noncontinuous and nonconvex programming problems. [ABSTRACT FROM AUTHOR]

Classification rules with a reserve judgment option provide a way to satisfy constraints on the misclassification probabilities when there is a high degree of overlap among the populations. Constructing rules which maximize the probability of correct classification while satisfying such constraints is a difficult optimization problem. This paper uses the form of the optimal solution to develop a relatively simple and computationally fast method for three populations which has a non parametric quality in controlling the misclassification probabilities. Simulations demonstrate that this procedure performs well. [ABSTRACT FROM AUTHOR]

In this paper we discuss optimality-based domain reductions for Global Optimization problems both from the theoretical and from the computational point of view. When applying an optimality-based domain reduction we can easily define a lower limit for the reduction which can be attained, but we can hardly guarantee that such limit is reached. Here, we theoretically prove that, for a nontrivial class of problems, appropriate strategies exist that are always able to reach this lower limit. On the other hand, we will also show that the same strategies lose this property as soon as we slightly enlarge the class of problems. Next, we perform computational experiments with a standard B&B approach applied to Linear Multiplicative Programming problems. We aim at establishing a good trade off between the quality of the domain reduction (the higher the quality, the lower the number of nodes in the B&B tree), and the computational cost of the domain reduction, and, thus, the effort per node of the B&B tree. [ABSTRACT FROM AUTHOR]

This paper considers the problem of minimizing a nonlinear objective function subject to a system of bipolar fuzzy relational equations with max- $T_{L}$ composition, where $T_{L}$ is the Łukasiewicz triangular norm. It shows that the feasible domain, i.e., the solution set of a system of bipolar fuzzy relational equations, can be reformulated as a system of 0-1 mixed integer inequalities. Consequently, such a type of optimization problems can be handled within the framework of 0-1 mixed integer optimization requiring no particular solving techniques. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present the topology optimization method to design the rotor and the tooth base in the stator of the permanent magnet (PM) excited machine with the improved high-speed features. The topological and shape sensitivity through the multi-level set method (MLSM) have been used to attain an innovative design of both the rotor and stator made of different materials. Design/methodology/approach – This framework is based on the application of the topological and the shape derivative, obtained by incorporating the adjoint variable method into the MLSM for the magnetoquasistatic system. The representation of the shape and their evolution during the iterative optimization process are obtained by the MLSM. Findings – To find the optimal configuration of a PM machine, the stator and rotor poles were simultaneously optimized by redistributing the iron and the magnet material over the design domains. In this way, it was possible to obtain an innovative design which allows to reduce mechanical vibration and the acoustic noise caused by the cogging torque, while taking the back electromotive force into account. Originality/value – The novelty of the proposed method is to apply the modified multi-level set algorithm with the total variation to the magnetoquasistatic optimization problem. Given the eddy currents phenomenon in the model of a PM machine, it was possible not only to optimize the structure of a PM machine but also to analyze electromagnetic losses distribution. [ABSTRACT FROM AUTHOR]

Pairs trading involves two cointegrated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered consisting of a short position in the outperforming stock and a long position in the underperforming one. Such a strategy bets the "spread" between the two would eventually converge. This paper is concerned with an optimal pairs-trade selling rule. In this paper, a difference of the pair is governed by a mean-reverting model. The trade will be closed whenever the difference reaches a target level or a cutloss limit. Given a fixed cutloss level, the objective is to determine the optimal target so as to maximize an overall return. This optimization problem is related to an optimal stopping problem as the cutloss level vanishes. Expected holding time and profit probability are also obtained. Numerical examples are reported to demonstrate the results. [ABSTRACT FROM AUTHOR]

The paper suggests a new-to the best of the author's knowledge-characterization of decisions, which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a prescribed angular radius. The main idea is to use the angle distances between the unit vector and points of utility space. A necessary and sufficient condition for the optimality in the form of an equation is derived. The first-order necessary optimality conditions are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constrained nonconvex nonsmooth optimization, in which both objective and constraint functions may not be convex or smooth. With the help of the penalty function, we transform the problem into an unconstrained one and design an algorithm in proximal bundle method in which local convexification of the penalty function is utilized to deal with it. We show that, if adding a special constraint qualification, the penalty function can be an exact one, and the sequence generated by our algorithm converges to the KKT points of the problem under a moderate assumption. Finally, some illustrative examples are given to show the good performance of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique. [ABSTRACT FROM AUTHOR]

In real linear spaces, partial orderings are usually generated by ordering cones. In many situations, however, such an ordering cone is too small with respect to the whole space. Therefore, in this paper, we extend the concept of ordering cones to a more general concept. For this purpose, we define a parameterized binary relation, based on a convex cone and a binary function. We investigate some geometrical and topological properties of this relation in detail. [ABSTRACT FROM AUTHOR]

Our study commemorates this event by presenting a retrospective of the publications related to the use of mathematical tools for the analysis of economic, ecological, and environmental phenomena. We analyzed 1257 scientific publications using bibliometric techniques to examine the most productive and influential authors and their contributions in the economic, ecological, and environmental fields. Co-authorship among the top authors and countries, co-occurrence of the keywords, bibliographic coupling of the documents and authors, and author co-citation were analyzed by applying network analysis techniques using VOSviewer software, identifying the intellectual structure of the research and the collaborative networks in the fields. The results show that mathematics has grown impressively in terms of publication and citation. The contributions come from all over the world, but the majority are from the People's Republic of China and Spain. The results also show themes and trends in the economic, environmental, and ecological fields and a predominant use of mathematical tools in optimization processes in order to rigorously substantiate the decisions of investors and policymakers. Thus, our study offers support for any researcher to understand the current state of the art and develop a comprehensive understanding of journal publications. [ABSTRACT FROM AUTHOR]

In the last decades, heuristic algorithms are widely used in solving problems in different fields of science and engineering. Most of these methods are inspired by natural phenomena, such as biological behaviours or physical principles. In this paper, a new optimization method based on the dynamic of sliding motion along a frictionless inclined plane is introduced. In the proposed algorithm, a collection of agents cooperate with each other and move toward better positions in the search space by employing Newton's second law and equations of motion. Our method is compared with other popular optimization algorithms and the results on 23 standard benchmark functions show its effectiveness in most cases. [ABSTRACT FROM AUTHOR]

Optimal reactive power planning is one of the major and important problems in electrical power systems operation and control. This is nothing but multi-objective, nonlinear, minimization problem of power system optimization. This paper presents the relevance of New Improved Differential Evolution (NIDE) algorithm to solve the Reactive Power Planning (RPP) problem based on Multi-objective optimization. Minimization of total cost of energy loss and cost of F A C T controlers installments are taken as the objectives incorporating (RPP) problem. With help of New Voltage Stability Index (NVSI), the critical lines and buses are identified to install the FACTS controllers. The optimal settings of the control variables of the generator voltages, transformer tap settings and provision and parameter settings of the FACT controllers SVC, TCSC, and UPFC are considered for reactive power planning. The approach applied to IEEE 30 and 72-bus Indian system for minimization of active power loss. Simulation results are compared with other optimization algorithm. [ABSTRACT FROM AUTHOR]

In multiple-hop MIMO relay systems, an end-to-end channel capacity is restricted by the bottleneck relay. Therefore, in order to obtain the high end-to-end channel capacity, we propose a simple mathematical method to optimize both distances and transmit powers simultaneously. Additionally, the end-to-end channel capacity of optimization based on an one-way and a two-ways transmissions is analyzed. The specific TDMA is proposed to control the transmission of all transmitters on MAC layer and then the distance and the transmit power are optimized based on MAC-PHY cross layer by the proposal particle filter method to obtain the higher end-to-end channel capacity. The calculation result indicates that there is the optimal number of relays that has the maximal end-to-end channel capacity and the trade-off between the end-to-end channel capacity and the delay time. [ABSTRACT FROM AUTHOR]

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption. [ABSTRACT FROM AUTHOR]

The article reviews the main situations one may encounter in constrained optimization of computer experiments, some of the corresponding existing tools and areas open for innovation. Topics discussed include the analytical formulas of the main criterion of L. Gramacy et al for the single constraint problem and the general behavior of the AL strategy and proposed modifications to improve its efficiency.

Many inverse problems can be formulated as split feasibility problems. To find feasible solutions, one has to minimize proximity functions. We show that the existence of minimizers to the proximity function for Censor-Elfving's split feasibility problem is equivalent to the existence of projections on appropriate convex sets and provide conditions under which such projections exist. These projections turn out to be the unique optimal solution of their Fenchel-Rockafellar duals and can be computed by the proximal point algorithm efficiently. Applications to linear equations and linear feasibility problems are given. [ABSTRACT FROM AUTHOR]

Constraint propagation techniques have heavily utilized interval arithmetic while the application of convex and concave relaxations has been mostly restricted to the domain of global optimization. Here, reverse McCormick propagation, a method to construct and improve McCormick relaxations using a directed acyclic graph representation of the constraints, is proposed. In particular, this allows the interpretation of constraints as implicitly defining set-valued mappings between variables, and allows the construction and improvement of relaxations of these mappings. Reverse McCormick propagation yields potentially tighter enclosures of the solutions of constraint satisfaction problems than reverse interval propagation. Ultimately, the relaxations of the objective of a non-convex program can be improved by incorporating information about the constraints. [ABSTRACT FROM AUTHOR]

The shortest path problem is among fundamental problems of network optimization. Majority of the optimization algorithms assume that weights of data graph's edges are pre-determined real numbers. However, in real-world situations, the parameters (costs, capacities, demands, time) are not well defined. The fuzzy set has been widely used as it is very flexible and cost less time when compared with the stochastic approaches. We design a bio-inspired algorithm for computing a shortest path in a network with various types of fuzzy arc lengths by defining a distance function for fuzzy edge weights using $$\alpha $$ cuts. We illustrate effectiveness and adaptability of the proposed method with numerical examples, and compare our algorithm with existing approaches. [ABSTRACT FROM AUTHOR]

Sufficient conditions for the existence of a solution to an abstract optimization problem in Banach spaces are given, which do not rely on convexity, regularity properties or a straightforward coerciveness assumption. Applications to sparsity-constrained optimization and to problems from mechanics are provided. [ABSTRACT FROM AUTHOR]