In a recent paper, Bauschke et al. study \(\rho \)-comonotonicity as a generalized notion of monotonicity of set-valued operators A in Hilbert space and characterize this condition on A in terms of the averagedness of its resolvent \(J_A.\) In this note we show that this result makes it possible to adapt many proofs of properties of the proximal point algorithm PPA and its strongly convergent Halpern-type

We consider scheduling problems such that the due date is assigned to a job, depending on its position, and the intervals between consecutive due dates are identical. The objective is to minimize the weighted number of tardy jobs or the total weighted tardiness. Both two-machine flow shop and single-machine cases are considered. We establish the computational complexity of each case, based on the relationship

We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm, DDMCuts, is based on the Gomory cuts and the dynamic version of the double description method. We describe the computer implementation of the algorithm and present the results of computational experiments comparing

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualifications to second-order cone programming and

Misinformation detection in Online Social Networks has recently become a critical topic due to its important role in restraining misinformation. Recent studies have showed that machine learning methods can be used to detect misinformation/fake news/rumors by detecting user’s behaviour. However, we can not implement this strategy for all users on a social network due to the limitation of budget. Therefore

In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best is based on significantly more variables and constraints

The multiple obnoxious facilities location problem is an extremely non-convex optimization problem with millions of local optima. It is a very challenging problem. We improved the best known solution for 33 out of 76 test instances. We believe that the results of many instances reported here are still not optimal and thus better objective function values exist. We challenge the optimization community

In this paper, we focus on the problem of minimizing the sum of nonconvex smooth component functions and a nonsmooth weakly convex function composed with a linear operator. One specific application is logistic regression problems with weakly convex regularizers that introduce better sparsity than the standard convex regularizers. Based on the Moreau envelope with a decreasing sequence of smoothing

This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex optimization problems with minimal requirements. We study the method of weighted dual averages (Nesterov in Math Programm 120(1): 221–259, 2009) in this setting and

In this paper, we consider the solution of global optimization problems involving hidden constraints. We present a novel deterministic derivative-free global optimization algorithm based on our recently introduced DIRECT-GL (Stripinis et al. in Optim Lett. 12(7):1699–1712, 2018). The new algorithm (DIRECT-GLh) incorporates two additional techniques for faster feasibility detection and solution improvement

In this paper, the connectedness of solution sets for generalized vector equilibrium problems via free-disposal sets (GVEPVF) in complete metric space is discussed. Firstly, by virtue of Gerstewitz scalarization functions and oriented distance functions, a new scalarization function \(\omega \) is constructed and some properties of it are given. Secondly, with the help of \(\omega \), the existence

Mobile ad hoc networks (MANETs) have been widely used for information distribution tasks. The radio communication channels that are established dynamically between the different terminals of these networks, like wireless sensors, ground vehicles, and autonomous assets (e.g. UAVs), allow for a flexible and efficient information distribution process. However, given the dynamic topology and limited bandwidth

In this paper, we introduce the k-generalized Steiner forest (k-GSF) problem, which is a natural generalization of the k-Steiner forest problem and the generalized Steiner forest problem. In this problem, we are given a connected graph \(G =(V,E)\) with non-negative costs \(c_{e}\) for the edges \(e\in E\), a set of disjoint vertex sets \({\mathcal {V}}=\{V_{1},V_{2},\ldots ,V_{l}\}\) and a parameter

Inverse optimization is the study of imputing unknown model parameters of an optimization problem using past observed solutions to that problem. In inverse linear programming, recent work uses multiple observations as input, while inverse integer programming has, to date, mostly focused on the case of a single observed data point or the case where a given cost vector needs to be minimally perturbed

This paper introduces and formulates a covering traveling salesman problem with profit arose in the last mile delivery. In this problem, a set of vertices including a central depot, customers and parcel lockers (PL) are given, and the goal is to construct a Hamiltonian cycle within a pre-defined cost over a subset of customers and/or PLs to collect maximum profits, each unvisited customer is covered

In this paper, we consider multiprocessor scheduling with submodular penalties to extend multiprocessor scheduling with rejection to submodular function. An instance of the problem is given by n jobs and m machines with each job having a certain processing time on a machine. We aim to find a subset R of rejected jobs, and assign each of other jobs to one of the m machines. The objective is to minimize

This paper studies linearly constrained least-square optimization problems in Hilbert spaces for which the KKT system is not necessarily available to analyze and compute the solution. The primary objective is to develop new qualitative and quantitative stability estimates for the regularization error in the conical regularization approach. To attain this goal, we associate the notion of stability with

We apply the t-linearization technique to the maximum diversity problem (MDP) and compare its performance with other well-known linearizations. We lift the t-constraints based on the cardinality restriction, derive valid inequalities for MDP, and show their usefulness to solve the problem within the t-linearization framework. We propose and computationally evaluate a branch-and-bound algorithm on benchmark

In a recent paper, Jiang et al. (Eng Optim 52(1):37–52, 2020) considered proportionate flowshop scheduling with position-dependent weights. For common and slack due-date assignment problems, they proved that both of these two problems can be solved in \(O(n^{2} \log n)\) time, where \(n\) is the number of jobs. The contribution of this paper is that we show that these two problems can be optimally

While measuring forecasting accuracy has been intensively studied by researchers, the consideration of sets of non-dominated solutions has not yet been explored in the literature. Even when considering measures that are in harmony, small changes in model parameters can result in a trained system capable of forecasting different time series characteristics. In this regard, this study shows how a set

This paper conducts a comparative study of proximal gradient methods (PGMs) and proximal DC algorithms (PDCAs) for sparse regression problems which can be cast as Difference-of-two-Convex-functions (DC) optimization problems. It has been shown that for DC optimization problems, both General Iterative Shrinkage and Thresholding algorithm (GIST), a modified version of PGM, and PDCA converge to critical

The Green Vehicle Routing Problem with Capacitated Alternative Fuel Stations assumes that, at each station, the number of vehicles simultaneously refueling cannot exceed the number of available pumps. The state-of-the-art solution method, based on the generation of all feasible non-dominated paths, performs well only with up to 2 pumps. In fact, it needs cloning the paths between every pair of pumps

We consider the quadratic optimization problem \(\max _{x \in C}\ x^{\mathrm {T}}Q x + q^{\mathrm {T}}x\), where \(C\subseteq {\mathbb {R}}^n\) is a box and \(r:= {{\,\mathrm{rank}\,}}(Q)\) is assumed to be \({\mathcal {O}}(1)\) (i.e., fixed). We show that this case can be solved in polynomial time for an arbitrary Q and \(q\). The idea is based on a reduction of the problem to enumeration of faces

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in the literature. Previous algorithmic solutions were typically nonconvex heuristics and were often developed in a case-by-case manner for specific structured affine

The paper is devoted to the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous (with a finite number of discontinuity points) and bounded

Banjac et al. (J Optim Theory Appl 183(2):490–519, 2019) recently showed that the Douglas–Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive iterates generated by the algorithm converges to certificates of primal and dual strong infeasibility. Their result was shown in a finite-dimensional

In the original publication of the article, the second author was missed to be added.

In this paper, we study the recently introduced Traveling Car Renter Problem. This latter is a generalization of the well-known traveling salesman problem, where a solution is a set of paths of different colors as well as an orientation of each path in such a way that the union forms a directed Hamiltonian circuit. Considering costs associated with all edges and all ordered pairs of nodes for each

This paper presents three reformulations for the well-known maximum capture location problem under multinomial logit choice. The problem can be cast as an integer fractional program and it has been the subject of several linear reformulations in the past. Here we develop two linear and a conic reformulation based on alternative treatments of fractional programs. Numerical experiments conducted on established

Given the costs and a feasible solution for a finite-dimensional linear program (LP), inverse optimization involves finding new costs that are close to the original and that also render the given solution optimal. Ahuja and Orlin employed the absolute sum norm and the maximum absolute norm to quantify distances between cost vectors, and applied duality to establish that the inverse LP problem can be

This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined

In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility location sets, a client location set of cardinality n and a non-negative integer \(q

In this paper, we develop optimality conditions and propose an algorithm for generalized fractional programming problems whose objective function is the maximum of finite ratios of difference of convex (dc) functions, with dc constraints, that we will call later, DC-GFP. Such problems are generally nonsmooth and nonconvex. We first give in this work, optimality conditions for such problems, by means

We introduce and study the notion of the \(\left( \sigma ,y\right) \)-conjugate of a proper \(\sigma \)-convex function. Some relations between the \(\sigma \)-subdifferentials and the Clarke–Rockafellar subdifferential are established. Also, we present some results regarding the \(\sigma \)-monotonicity of the \(\sigma \)-subdifferential of a function and its \(\sigma \)-convexity. Moreover, we obtain

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