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

The multi-depot open vehicle routing problem (MDOVRP) is a hard combinatorial optimization problem belonging to the vehicle routing problem family. It considers vehicles departing from different depots to deliver goods to customers without requiring to return to the depots once all customers have been served. The aim of this work is to provide a new two-index-based mathematical formulation for the

This paper investigates a three-competing group scheduling problem on serial-batching machines considering the setup time of groups and batches, as well as the job-dependent deteriorating effect, where the setup time of groups and batches depends on their own corresponding start time and deterioration rate, and the jobs’ actual processing time depends on their starting time and deterioration rate.

In this paper we study two types of strong set-valued equilibrium problems in Hausdorff locally convex topological vector spaces. Under suitable assumptions, stability in the sense of Hausdorff continuity of solutions is established. Main results are applied to Browder variational inclusions.

We present some characterizations of the ordered weighted \(\ell _1\) norm (aka sorted \(\ell _1\) norm) and of the vector Ky-Fan norm as solutions to linear programs involving reasonably many variables and constraints. Such linear characterizations can be exploited to recast and effortlessly solve a variety of convex optimization problems involving these norms. Similar linear characterizations are

We consider the general problem formulation as the minimization of the sum of the numbers of the feasible subset of cardinality n out of the set of N numbers. Asymmetric travelling salesman problem, assignement problem and the problem of minimization of the sum of n numbers out of the set of N numbers can be formulated in these terms. The input of all these problems can be represented as the point

In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.

In this paper, we study optimal control problems containing ordinary control systems, linear with respect to a control variable, described by fractional Dirichlet and Dirichlet–Neumann Laplace operators and a nonlinear integral performance index. The main result is a theorem on the existence of optimal solutions for such problems. In our approach we use a characterization of a weak lower semicontinuity

In this study, we introduce the Traveling Car Renter with Passengers (CaRSP), an extension of the Traveling Car Renter Problem (CaRS). The latter generalizes the Traveling Salesman Problem (TSP) by allowing several cars with different costs to be available for use during the salesman’s tour. In the CaRSP, passengers are allowed in the salesman’s car and share trip expenses with the driver. Passengers

This paper investigates the combinatorial nonlinear programming model that DiDi proposed for solving their driver-order matching problem. The model is reformulated to an equivalent continuous nonlinear program which is amenable to efficient commercial solvers. A backward induction procedure for computing the lower bound is also proposed. Computational experiments demonstrate that the local solution

A classic result of Banach states that the supreme of a multivariate homogenous polynomial is equivalent to that of its associated symmetric multilinear form over unit balls. Using the language of higher-order tensors in finite-dimensional spaces, this means that for a symmetric tensor, its largest singular value is in fact equivalent to the largest magnitude of its eigenvalues. This note strengthens

We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality

In this paper we introduce a new parameterized Quadratic Decision Rule (QDR), a generalisation of the commonly employed Affine Decision Rule (ADR), for two-stage linear adjustable robust optimization problems with ellipsoidal uncertainty and show that (affinely parameterized) linear adjustable robust optimization problems with QDRs are numerically tractable by presenting exact semi-definite program

In this paper, we show that the weighted vertex coloring problem can be solved in polynomial on the sum of vertex weights time for \(\{P_5,K_{2,3}, K^+_{2,3}\}\)-free graphs. As a corollary, this fact implies polynomial-time solvability of the unweighted vertex coloring problem for \(\{P_5,K_{2,3},K^+_{2,3}\}\)-free graphs. As usual, \(P_5\) and \(K_{2,3}\) stands, respectively, for the simple path

A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra’s algorithm. In this paper, we provide sufficient conditions for Dykstra’s algorithm to converge rapidly, in finitely many steps. We also analyze the behaviour of Dykstra’s algorithm applied to a line and a square. This case study reveals stark similarities to the method of alternating

In this paper, we present an improved methodology to compute the \(\omega \)-primality of a numerical semigroup. The approach is based on exploiting the structure of the problem on a resolution method for optimizing a linear function over the set of efficient solutions of a multiple objective integer linear programming problem. The numerical experiments show the efficiency of the proposed technique

We decompose the copositive cone \(\mathcal {COP}^{n}\) into a disjoint union of a finite number of open subsets \(S_{{\mathcal {E}}}\) of algebraic sets \(Z_{{\mathcal {E}}}\). Each set \(S_{{\mathcal {E}}}\) consists of interiors of faces of \(\mathcal {COP}^{n}\). On each irreducible component of \(Z_{{\mathcal {E}}}\) these faces generically have the same dimension. Each algebraic set \(Z_{{\mathcal

We study a variant of the competitive facility location problem, in which a company is to locate new facilities in a market where competitor’s facilities already exist. We consider the scenario where only a limited number of possible attractiveness levels is available, and the company has to select exactly one level for each open facility. The goal is to decide the facilities’ locations and attractiveness

In this work, we propose a new modified Popov’s method by using inertial effect for solving the variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration as well as it does not need to the prior knowledge of the Lipschitz constants of the variational

The Curriculum Based university Course Timetabling (CCT) problem consists in determining the best scheduling of university course lessons in a given time interval, assigning the lessons of each course to classrooms and time periods, so that a series of constraints is satisfied. These constraints are divided into two categories: hard constraints, necessary so that the programming can actually be implemented

In this paper, we consider the k-sink location problem in a path network with the goal of optimizing a combinational function of the maximum completion time and the total completion time. Let \(P=\left( V,E\right) \) be an undirected path network with n vertices. Each vertex has a positive weight, indicating the initial amount of supplies, and each edge has a positive length and a uniform capacity

This short paper describes a simple subgradient-based techniques for deriving bounds on the optimal solution value when using the ADMM to solve convex optimization problems. The technique requires a bound on the magnitude of some optimal solution vector, but is otherwise completely general. Some computational examples using LASSO problems demonstrate that the technique can produce steadily converging

Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the cosine measure and convergence properties of certain DFO algorithms are intimately linked to the value of this measure. However, it is unclear how to compute the cosine

The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using

This note advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite dimensions, we study general prox-bounded functions and then focus on some useful classes such as piecewise functions and Lipschitz continuous functions. The thresholds

This paper mainly investigates the locally Lipschitz optimization problem (LLOP) with \(l_0\)-regularization in a finite dimensional space, which is generally NP-hard but highly applicable in statistics, compressed sensing and deep learning. First, we introduce two classes of stationary points for this problem: subdifferential-stationary point and proximal-stationary point. Secondly, based on these

In this paper, we propose a regularization projection method for solving a bilevel variational inequality problem in a Hilbert space. We first describe how to incorporate the regularization technique and the modified subgradient extragradient—like method, and then establish the strong convergence of the resulting algorithm under some suitable conditions. The new algorithm requires to compute only one

In this paper, we propose and study a new notion of local error bounds for a convex inequalities system defined in terms of a minimal time function. This notion is called generalized local error bounds with respect to F, where F is a closed convex subset of the Euclidean space \({\mathbb {R}}^n\) satisfying \(0\in F\). It is worth emphasizing that if F is a spherical sector with the apex at the origin

This paper presents a new mathematical programming model and a solution approach for a special class of graph partitioning problem. The problem studied here is in the context of distributed web search, in which a very large world-wide-web graph is partitioned to improve the efficiency of webpage ranking (known as PageRank). Although graph partitioning problems have been widely studied and there have

For single-commodity networks, the increase of the price of anarchy is bounded by a factor of \((1+\varepsilon )^p\) from above, when the travel demand is increased by a factor of \(1+\varepsilon \) and the latency functions are polynomials of degree at most p. We show that the same upper bound holds for multi-commodity networks and provide a lower bound as well.

This works investigates a conceptual algorithm for computing critical points of nonsmooth nonconvex optimization problems whose objective function is the sum of two locally Lipschitzian (component) functions. We show that upon additional assumptions on the component functions and or feasible set, the given algorithm extends several well-known optimization methods.

We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed framework includes two-stage decision dependent distributionally robust stochastic programming as a special case. Decision dependent generalizations of five types

This paper aims at presenting the multiple depot vehicle scheduling problem with heterogeneous fleet and time windows (MDHFVSP-TW). We used a time-space network (TSN) to perform the modeling of MDHFVSP-TW, along with two methodologies to reduce its size and, therefore, its complexity. Along with size reduction methods, a mixed integer programming (MIP) heuristic with variable fixation was presented

Surrogate model assisted evolutionary algorithms (SAEAs) are metamodel-based strategies usually employed on the optimization of problems that demand a high computational cost to be evaluated. SAEAs employ metamodels, like Kriging and radial basis function (RBF), to speed up convergence towards good quality solutions and to reduce the number of function evaluations. However, investigations concerning

In this paper, we propose a theoretical framework of a predictor-corrector interior-point method for linear optimization based on the one-norm wide neighborhood of the central path, focusing on infeasible corrector steps. Here, we call the predictor-infeasible corrector algorithm. At each iteration, the proposed algorithm computes an infeasible corrector step in addition to the Ai-Zhang search directions

We consider Pareto-scheduling with two competing agents A and B on a single machine, in which each job has a positional due index and a deadline. The jobs of agents A and B are called the A-jobs and B-jobs, respectively, where the A-jobs have a common processing time, while the B-jobs are restricted by their precedence constraint. The objective is to minimize a general sum-form objective function of

We develop an optimization model to provide a fair allocation of multiple resources to multiple users. All resources might not be suitable to all users. We develop a notion of fairness, and then provide a general class of functions achieving it. Next, we develop more restricted notions of fairness—special cases of which exist in literature. Finally, we distinguish between scarce and abundant resources

In this paper, we consider a store that sells two vertically differentiated items that might substitute each other. These items do not only differ in quality and price, but they also target two different customer segments. Items deteriorate over time and might require price adjustments to avoid cannibalization. We provide closed-form solutions for pricing and ordering of these items that lead to key

In this work, we present and analyze C-SAGA, a (deterministic) cyclic variant of SAGA. C-SAGA is an incremental gradient method that minimizes a sum of differentiable convex functions by cyclically accessing their gradients. Even though the theory of stochastic algorithms is more mature than that of cyclic counterparts in general, practitioners often prefer cyclic algorithms. We prove C-SAGA converges

We study a scheduling problem with linear deterioration of job processing times. We consider parallel identical machines. The objective is minimum total load, i.e., minimum total processing times on all the machines. We propose a simple heuristic of a greedy type for this NP-hard problem. A lower bound based on the geometric mean of the job deterioration factors is also introduced. The greedy heuristic

We develop a power penalty approach to the discrete Hamilton–Jacobi–Bellman (HJB) equation in \( \mathbb {R}^N \) in which the HJB equation is approximated by a nonlinear equation containing a power penalty term. We prove that the solution to this penalized equation converges to that of the HJB equation at an exponential rate with respect to the penalty parameter when the control set is finite and

In the original publication of the article, the name of the corresponding author was incorrectly published as “Amir Ahamdi”.

In this paper, a necessary and sufficient condition, such as the Pontryagin’s maxi-mum principle for a fractional optimal control problem with concentrated parameters, is given by the ordinary fractional differential equation with a coefficient in weighted Lebesgue spaces. We discuss a formulation of fractional optimal control problems by a fractional differential equation in the sense of Caputo fractional