Recently, the estimation problem of upper and lower bounds of the solution set of the tensor complementarity problem has been studied when the tensor involved is a strictly semi-positive tensor or one of its subclasses. This paper aims to study such an estimation problem in a larger scope. First, we propose a lower bound formula under the condition that the tensor complementarity problem has a solution

This work proposes a bi-objective mathematical optimization model and a two-stage heuristic for a real-world application of the heterogeneous Dynamic Dial-a-Ride Problem with no rejects, i.e., a patient transportation system. The problem consists of calculating route plans to meet a set of transportation requests by using a given heterogeneous vehicle fleet. These transportation requests can be either

Beside of cryptography-the primary traditional methods for ensuring information security and confidentiality, the appearance of the physical layer security approach plays an important role for not only enabling the data transmission confidentially without relying on higher-layer encryption, but also enhancing confidentiality of the secret key distribution in cryptography. Many techniques are employed

Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human–AI interaction system etc. In this paper, we design a hybrid extractive sentence compression model combining a probability language model and a parse tree language model for compressing sentences by guaranteeing the syntax correctness of the compression results

In this paper, we examine the properly twice epi-differentiability and compute the second order epi-subderivative of the indicator function to a class of sets including the finite union of parabolically derivable and parabolically regular sets. In this way, we provide no-gap second order optimality conditions for a disjunctive constrained problem. Moreover, we derive applications of our results to

We consider the maximum shortest path interdiction problem by upgrading edges on trees under Hamming distance (denoted by (MSPITH)), which has wide applications in transportation network, network war and terrorist network. The problem (MSPITH) aims to maximize the length of the shortest path from the root of a tree to all its leaves by upgrading edge weights such that the upgrade cost under sum-Hamming

In this paper, we study the extended trust-region subproblem in which the trust-region intersects the ball with m linear inequality constraints (m-eTRS). We assume that the linear constraints do not intersect inside the ball. We show that the optimal solution of m-eTRS can be found by solving one TRS, computing the local non-global minimizer of TRS if it exists and solving at most two TRSs with an

The vertex colourability problem is to determine, for a given graph and a given natural k, whether it is possible to split the graph’s vertex set into at most k subsets, each of pairwise non-adjacent vertices, or not. A hereditary class is a set of simple graphs, closed under deletion of vertices. Any such a class can be defined by the set of its forbidden induced subgraphs. For all but four hereditary

In this paper, we study the absolute value equation (AVE) \(Ax-b=|x|\). One effective approach to handle AVE is by using concave minimization methods. We propose a new method based on concave minimization methods. We establish its finite convergence under mild conditions. We also study some classes of AVEs which are polynomial time solvable.

In the sequel, we outline necessary and sufficient condition to the existence of extremas of a function on a self-similar set, and we describe discrete gradient algorithm to find the extrema.

The paper deals with a Berge equilibrium (Théorie générale des jeux à-personnes, Gauthier Villars, Paris, 1957; Some problems of non-antagonistic differential games, 1985) in the bimatrix game for mixed strategies. Motivated by Nash equilibrium (Ann Math 54(2):286, 1951; Econometrica 21(1):128–140, 1953), we prove an existence of Berge equilibrium in the bimatrix game. Based on Mills theorem (J Soc

During major infectious disease outbreak, such as COVID-19, the goods and parcels supply and distribution for the isolated personnel has become a key issue worthy of attention. In this study, we propose a delivery problem that arises in the last-mile delivery during major infectious disease outbreak. The problem is to construct a Hamiltonian tour over a subset of candidate parking nodes, and each customer

In this paper, we present the problem in which a municipal company operating in the waste management sector willing to encourage users to use differentiated waste collection facilities, designs a utility user function to attain such a goal. The problem is modeled in terms of bilevel optimization where the leader is the municipal firm which aims at maximizing the concurrent fraction of user waste demand

Researchers and practitioners have addressed many variants of facility locations problems. Each location problem can be substantially different from each other depending on the objectives and/or constraints considered. In this paper, the bi-objective obnoxious p-median problem (Bi-OpM) is addressed given the huge interest to locate facilities such as waste or hazardous disposal facilities, nuclear

In this paper, we present necessary/sufficient conditions for the convex polynomial programming (CPP) problems. Some new stability results for parametric CPP problems are characterized under a regular condition. We give a positive answer for the open question in Kim et al. (Optim Lett 6:363–373, 2012) for the solution existence of convex quadratic programming problems.

The Fixed-Tree BMEP (FT-BMEP) is a special case of the Balanced Minimum Evolution Problem (BMEP) that consists of finding the assignment of a set of n taxa to the n leaves of a given unrooted binary tree so as to minimize the BMEP objective function. Deciding the computational complexity of the FT-BMEP has been an open problem for almost a decade. Here, we show that a few modifications to Fiorini and

The purpose of this paper is to introduce a new modified subgradient extragradient method for finding an element in the set of solutions of the variational inequality problem for a pseudomonotone and Lipschitz continuous mapping in real Hilbert spaces. It is well known that for the existing subgradient extragradient methods, the step size requires the line-search process or the knowledge of the Lipschitz

The purpose of this short note is to show that the Christoffel–Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. Geometric interpretations and algorithmic consequences are mentioned.

This paper examines a new model for hub location known as the hub location routing problem. The problem shares similarities with the well studied uncapacitated single allocation p-hub median problem except that the hubs are now connected to each other by a cyclical path (or tour) known as the global route, each cluster of non-hub nodes and assigned hub is also connected by a single tour known as a

In job-shop manufacturing systems, an efficient production schedule acts to reduce unnecessary costs and better manage resources. For the same purposes, modern manufacturing cells, in compliance with industry 4.0 concepts, use material handling systems in order to allow more control on the transport tasks. In this paper, a job-shop scheduling problem in vehicle based manufacturing facility that is

We consider the Max-Cut problem on an undirected graph \(G=(V,E)\) with \(|V|=n\) nodes and \(|E|=m\) edges. We investigate a linear size MIP formulation, referred to as (MIP-MaxCut), which can easily be derived via a standard linearization technique. However, the efficiency of the Branch-and-Bound procedure applied to this formulation does not seem to have been investigated so far in the literature

In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) \(Ax-B|x|=b\) with \(A, B\in \mathbb {R}^{n\times n}\) from the optimization field are first presented, which cover the fundamental theorem for the unique solution of the linear system \(Ax=b\) with \(A\in \mathbb {R}^{n\times n}\). Not only that, some new sufficient

The double row layout problem (DRLP) occurs in automated manufacturing environments, where a material-handling device transports materials among machines arranged in a double-row layout, i.e. a layout in which the machines are located on either side of a straight line corridor. The DRLP is how to minimize the total cost of transporting materials between machines. The problem is NP-Hard and one great

Nowadays more and more complex railway systems can operate efficiently only if we have tools for planning their maintenance. Train accidents are mainly caused by infrastructure problems, or more specifically by track geometry failures.In this paper, we present a support decision system for forecasting the deterioration of track geometry. Two types of defects can be identified for each railway track

If \(S=\{v_1,\ldots , v_k\}\) is an ordered subset of vertices of a connected graph G and e is an edge of G, then the vector \(r_G(e|S) = (d_G(v_1,e), \ldots , d_G(v_k,e))\) is the edge metric S-representation of e. If the vertices of G have pairwise different edge metric S-representations, then S is an edge metric generator for G. The cardinality of a smallest edge metric generator is the edge metric

The discrete formulation of Particle Swarm Optimization (PSO) is nowadays widely used. The paper presents a continuous formulation of the PSO problem along with its analytic solution. The aim is to verify whenever an amelioration of the standard discrete PSO is achievable by employing its continuous counterpart. The convergence of the proposed continuous PSO scheme is analyzed accounting for variation

In this paper, we propose a computationally efficient approach for solving complex multicriteria lexicographic optimization problems, which can be complicated by the multiextremal nature of the efficiency criteria and extensive volume of computations required to calculate the criteria values. The formulation of problems is assumed to be the subject to change as well, which, in turn, may require solving

In this paper, we consider the submodular multicut problem in trees with linear penalties (SMCLP(T) problem). In the SMCLP(T) problem, we are given a tree \(T=(V,E)\) with a submodular function \(c(\cdot ): 2^{E}\rightarrow \mathbb {R}_{\ge 0}\), a set of k distinct pairs of vertices \(P=\{(s_1,t_1),(s_2,t_2),\ldots ,(s_k,t_k)\}\) with non-negative penalty costs \(\pi _{j}\) for the pairs \((s_j,t_j)\in

We consider a class of inertial second order dynamical system with Tikhonov regularization, which can be applied to solving the minimization of a smooth convex function. Based on the appropriate choices of the parameters in the dynamical system, we first show that the function value along the trajectories converges to the optimal value, and prove that the convergence rate can be faster than \(o(1/t^2)\)

Linear bilevel optimization problems are often tackled by replacing the linear lower-level problem with its Karush–Kuhn–Tucker conditions. The resulting single-level problem can be solved in a branch-and-bound fashion by branching on the complementarity constraints of the lower-level problem’s optimality conditions. While in mixed-integer single-level optimization branch-and-cut has proven to be a

One of the practical application in cellular manufacturing systems is the cell formation problem (CFP). Its main idea is to group machines into cells and parts into part families in a way that the number of exceptional elements and the number of voids are minimized. In literature, it is proved that p-median is an efficient mathematical programming model for solving CF problems. In the present work

Several variants of the classical Constrained Shortest Path Problem have been presented in the literature so far. One of the most recent is the k-Color Shortest Path Problem (\(k\)-CSPP), that arises in the field of transmission networks design. The problem is formulated on a weighted edge-colored graph and the use of the colors as edge labels allows to take into account the matter of path reliability

The aim of this paper is to introduce a new inertial Tseng’s extragradient algorithm for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in real Hilbert spaces. We prove a strong convergence theorem for the proposed algorithm under suitable assumptions imposed on the parameters. Finally, we give some numerical

It is well known that a quadratic programming minimization problem with one negative eigenvalue is NP-hard. However, in practice one may expect such problems being not so difficult to solve. We suggest to make a single partition of the feasible set in a concave variable only so that a convex approximation of the objective function upon every partition set has an acceptable error. Minimizing convex

In the field of automatic programming (AP), the solution of a problem is a program, which is usually represented by an AP-tree. A tree is built using functional and terminal nodes. For solving AP problems, we propose a new neighborhood structure that adapts the classical “elementary tree transformation” (ETT) into this specific AP-tree. The ETT is the process of removing an edge and adding another

In this paper, we consider a problem of optimal covering a barrier in the form of a line segment with equal circles distributed in a plane by moving their centers onto the segment or the line containing a segment. We require the neighboring circles in the cover to touch each other. The objective is to minimize the total traveled by circles Euclidian distance. The complexity status of the problem is

This paper addresses a real-life personnel scheduling problem in the context of Covid-19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive groups to reduce the risk of contagion

The generalized independent set problem (GISP) can be conceived as a relaxation of the maximum weight independent set problem. GISP has a number of practical applications, such as forest harvesting and handling geographic uncertainty in spatial information. This work presents an iterated local search (ILS) heuristic for solving GISP. The proposed heuristic relies on two new neighborhood structures

The Order Processing in Picking Workstations is a real problem derived from the industry in the context of supply chain management. It looks for an efficient way to process orders arriving to a warehouse by minimizing the number of movements of goods, stored in containers in the warehouse, from their storage location to the processing zone. In this paper, we tackle this real optimization problem by

Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (J Optim Theory Appl 19(2):261–281, 1976), a sequence of lower bounds which converges to the optimal objective value may be obtained with specially constructed finite approximations of the constraint set. In Mitsos (Optimization

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely used in data analysis. To gain a better understanding of why spectral clustering is successful, Peng et al. (In: Proceedings of the 28th conference on learning theory

Kurz and Napel (Optim Lett 10(6):1245–1256, 2015, https://doi.org/10.1007/s11590-015-0917-0) proved that the voting system of the EU council (based on the 2014 population data) cannot be represented as the intersection of six weighted games, i.e., its dimension is at least 7. This set a new record for real-world voting rules and the authors posed the exact determination as a challenge. Recently, Chen

In this paper, we introduce some new approximation projection algorithms for solving monotone equilibrium problems over the intersection of fixed point sets of demicontractive mappings. By combining subgradient projection methods and hybrid steepest descent methods, strong convergence of the algorithms to a solution is shown in a real Hilbert space. Some numerical illustrations and comparisons are

The facility layout problem is concerned with finding an arrangement of non-overlapping indivisible departments within a facility so as to minimize the total expected flow cost. In this paper we consider the special case of multi-row layout in which all the departments are to be placed in three or more rows, and our focus is on, for the first time, solutions for large instances. We first propose a

In this note, we consider the iteration complexity of solving strongly convex multi-objective optimization problems. We discuss the precise meaning of this problem, noting that its definition is ambiguous, and focus on the most natural notion of finding a set of Pareto optimal points across a grid of scalarized problems. We prove that, in most cases, performing sensitivity based path-following after

Based on the notation of Mordukhovich subdifferentials (Mordukhovich in Variational analysis and generalized differentiation I: basic theory, Springer, Berlin, 2006; Variational analysis and generalized differentiation II: applications, Springer, Berlin, 2006; Variational analysis and applications, Springer, Berlin, 2018), we establish strong Karush–Kuhn–Tucker type necessary optimality conditions

Nonnegative matrix factorization (NMF) has become a popular method for establishing a low-dimensional approximation of a two-mode (nonnegative) data matrix and, in some instances, to also establish partitions for the objects associated with the two modes of the matrix. Although similar to singular-value-decomposition, as its name implies, NMF requires nonnegative elements for the factors and this assures

A new stochastic primal-dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions / operators that enter the optimization problem are given as statistical expectations. These expectations are unknown but revealed across time through i.i.d realizations. The proposed algorithm is proven to converge to a saddle point of the Lagrangian function. In the

We consider the online scheduling on an unbounded (drop-line) parallel batch machine to minimize the time by which all jobs have been delivered. In this paper, all jobs arrive over time and the running batches are allowed limited restart. Here limited restart means that a running batch which contains restarted jobs cannot be restarted again. A drop-line parallel batch machine can process several jobs

In the context of support vector machines, identifying the support vectors is a key issue when dealing with large data sets. In Camelo et al. (Ann Oper Res 235:85–101, 2015), the authors present a promising approach to finding or approximating most of the support vectors through a procedure based on sub-sampling and enriching the support vector sets by nearest neighbors. This method has been shown

In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the distance of the initial iterate to the closest fixed point divided by the number of iterations plus one.

Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper addresses the complexity of uncapacitated multi-plant lot-sizing problems. We consider a multi-item uncapacitated multi-plant lot-sizing problem with fixed transfer costs and show that

The multidimensional knapsack problem (MKP) is an NP-hard combinatorial optimization problem whose solution consists of determining a subset of items of the maximum total profit that does not violate capacity constraints. Due to its hardness, large-scale MKP instances are usually a target for metaheuristics, a context in which effective feasibility maintenance strategies are crucial. In 1998, Chu and

A family of (k, m)-ary trees was firstly introduced by Du and Liu when they studied hook length polynomial for plane trees. Recently, Amani and Nowzari-Dalini presented a generation algorithm to produce (k, m)-ary trees of order n encoding by Z-sequences in reverse lexicographic order. In this paper, we propose a loopless algorithm to generate all such Z-sequences in Gray code order. Hence, the worst-case

We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on the centrality equation of the central path system and Newton’s method is applied on this modified system. This technique was offered by Zsolt Darvay for linear optimization in 2002. Darvay first used the

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence

In this paper, a vector network equilibrium problem with uncertain demands and capacity constraints of arcs is investigated, where the demands belong to a closed interval. By considering two kinds of vector cost functions, i.e., the costs of each path depend on the whole path flow and the path flow itself, the corresponding (weak) vector equilibrium principles are proposed. For the former, some existence

Transportation auctions are increasingly made online and the bidding time intervals are becoming much shorter. From the carriers’ perspective, bid determination problems need to be solved more quickly due to the increasing number of auctions in the online transportation marketplace for their survivability. In this research, we study the bid price determination problem of truckload (TL) carriers participating

In this paper we consider a proximal method of multipliers (PMM) for a nonlinear second-order cone optimization problem. With the assumptions of constraint nondegeneracy, strict complementarity and second-order sufficient condition, we estimate the local convergence rate of PMM to be linear or superlinear, which depends on the strategy of parameter selection.

A cruise company faces three decision problems: at a strategic level, to decide in which maritime area and in which season window to locate each ship of its fleet; at a tactical level, given a ship in a maritime area and in a season window, to decide which cruises to offer to the customers; at an operational level, to determine the day-by-day itinerary, in terms of transit ports, arrival and departure