This paper considers an assessment and evaluation of speech sound pronunciation quality in computer-aided language learning systems. We examine the gain optimization of spectral distortion measures between the speech signals of a native speaker and a learner. During training, a learner has to achieve stable pronunciation of all sounds. This is measured by computing the distances between the sounds

In this paper, we introduce and investigate a new regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. The normalization argument in asymptotic analysis enables us to study the existence as well as the stability of solutions of these problems. We prove a Frank–Wolfe type theorem for regular optimization problems and an Eaves type theorem for

This paper is devoted to the investigation of a class of uncertain multiobjective fractional semi-infinite optimization problems (\(UMFP \), for brevity). We first obtain, by combining robust optimization and scalarization methodologies, necessary and sufficient optimality conditions for robust approximate weakly efficient solutions of (\(UMFP \)). Then, we introduce a Mixed type approximate dual problem

The purpose of this article is to establish some results on the existence and generic stability of solution sets of the controlled system for multiobjective generalized games in infinite-dimensional spaces. First, we introduce a class of the controlled system for multiobjective generalized games. Afterward, we establish some conditions for existence of the solution set to this problem using the Ka

Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has \(\mathbb {R}_+\) as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions

This paper introduces a new subclass of convex functions called uniformly convex functions [this class is a slight extension of the class introduced earlier by Zălinescu (J Math Anal Appl 95:344–374, 1983; Convex analysis in general vector spaces, World Scientific, Singapore)] and studies some of its properties. It also defines a new subdifferentiability called \((\phi ,c)\)-subdifferentiability and

In this paper, we propose optimization models to address flexible staff scheduling problems and some main issues arising from efficient workforce management during the Covid-19 pandemic. The adoption of precautionary measures to prevent the pandemic from spreading has raised the need to rethink quickly and effectively the way in which the workforce is scheduled, to ensure that all the activities are

In this paper, to economically and fast solve the linear complementarity problem, based on a new equivalent fixed-point form of the linear complementarity problem, we establish a class of new modulus-based matrix splitting methods, which is different from the previously published works. Some sufficient conditions to guarantee the convergence of this new iteration method are presented. Numerical examples

In our current fast-paced era, customers are often willing to pay extra premium for shorter lead times, which motivates further research on the scheduling problem with due-date assignment and customer-specified lead times. As part of this effort, we extend the classic minsum ‘DIF’ scheduling model to allow optional job-rejection, thus adding an important component of real-life applications, namely

Prediction tasks in personalized medicine require models that combine accuracy and interpretability. We propose an integer optimization approach for building sparse regression models with enforced coordination, using data partitioned among leaves in a prediction tree. We show that the method recovers the true underlying relationship between observations and target variables in large-scale synthetic

Mathematical programming formulations are developed for determining chains of organ-donation exchange pairs in a compatibility graph where pairwise exchanges may fail. The objective is to maximize the expected value where pairs are known to fail with given probabilities. In previous work, namely that of Dickerson et al. (Manag Sci 65(4):323–340, 2019) this NP-hard problem was solved heuristically or

We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters provides much more flexibility, allows one to adaptively and independently take into account the violation of each constraint during optimization process, and often

In this article, we obtain controls that give the time-optimal trajectories for a Dubins airplane in the presence of fixed and moving obstacles. Using an exact penalty function method, we show the existence of the control variable for a Dubins airplane with given initial and final positions so that the airplane could reach its destination in the shortest time while avoiding fixed and moving obstacles

In this paper, we develop a unified convergence analysis framework for the Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in Tran-Dinh et al. (SIAM J Optim 28(1):96–134, 2018). Unlike Tran-Dinh et al. (SIAM J Optim 28(1):96–134, 2018), the new analysis covers three settings in a single algorithm: general convexity, strong convexity, and strong convexity and smoothness. Moreover, we

We consider a multiple-depots extension of the classic Hamiltonian path problem where k salesmen are initially located at different depots. To the best of our knowledge, no algorithm for this problem with a constant approximation ratio has been previously proposed, except for some special cases. We present a polynomial algorithm with a tight approximation ratio of \(\max \left\{ \frac{3}{2},2-\frac{1}{k}\right\}

Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same

In this paper we consider a resource-constrained scheduling problem on two parallel dedicated machines with given fixed processing sequences of jobs assigned to each one of the machines. The problem is to determine the starting times of all jobs, subject to the resource constraint, in order to minimize some given performance measure. Lin et al. (J Sched 19(2):153–163, 2016) showed that the problem

Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the US’s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A

We consider graphs, which and all induced subgraphs of which possess the following property: the maximum number of disjoint paths on k vertices equals the minimum cardinality of vertex sets, covering all paths on k vertices. We call such graphs König for the k-path and all its spanning supergraphs. For each odd k, we reveal an infinite family of minimal forbidden subgraphs for them. Additionally, for

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program (\({\textsc {MINLP}}\)) context. We show that the red refinement meets sufficient convergence conditions for a known \({\textsc {MINLP}}\) solution framework that is essentially based on solving piecewise linear relaxations. In

The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. This problem is APX-hard in the general metric case but admits polynomial-time approximation schemes in the geometric setting, when the edge weights are induced by a vector norm in fixed-dimensional real space. We propose the first approximation

In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov (Optim Methods Softw 27(4–5): 893–917, 2012) introduced a 4-self-concordant barrier for the power cone, also known as Koecher’s cone. In his PhD thesis, Chares (Cones and interior-point algorithms for structured convex optimization involving powers and exponentials, PhD thesis, Universite catholique

Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer

We revisit the classic supporting hyperplane illustration of the duality gap for non-convex optimization problems. It is refined by dissecting the duality gap into two terms: the first measures the degree of near-optimality in a Lagrangian relaxation, while the second measures the degree of near-complementarity in the Lagrangian relaxed constraints. We also give an example of how this dissection may

We establish a general duality theorem in a generalized conjugacy framework, which generalizes a classical result on the minimization of a convex function over a closed convex cone. Our theorem yields two quasiconvex duality schemes; one of them is of the surrogate duality type and is applicable to problems having an evenly quasiconvex objective function, whereas the other one is applicable to problems

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local differential privacy noise. The radius of the ambiguity set is selected based on privacy budget, spread of data, and size of the problem. Machine learning with private

The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank constraint into a product of two matrices via the Burer–Monteiro factorization. Then, we add the difference of the two matrices, with a penalty parameter, to the objective

Support vector machines with ramp loss (\(L_r\)-SVM) have attracted considerable attention due to the robustness of the ramp loss. However, the corresponding optimization problem is non-convex, and the given Karush–Kuhn–Tucker (KKT) conditions are only first-order necessary conditions. To enrich the optimality theory of \(L_r\)-SVM, we first introduce and analyze the proximal operator for the ramp

We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We present the first fully polynomial-time approximation scheme for the product knapsack problem, which is known to be weakly NP-hard. Moreover, we analyze

Classical facility location models can generate solutions that do not maintain consistency in the set of utilized facilities as the number of utilized facilities is varied. We introduce the concept of nested facility locations, in which the solution utilizing p facilities is a subset of the solution utilizing q facilities, for all \(i \le p < q \le j\), given some lower limit i and upper limit j on

We consider the problem of moving a connected set of railcars, which we refer to as a train, from an origin layout to a destination layout in a railyard, accounting for the special structure of the railyard network and the length and orientation of the train. We propose a novel shortest path algorithm for determining a sequence of moves that minimizes the total distance (and associated time) required

Protecting wildlife corridors is a common management problem in regions of industrial forestry. In boreal Canada, human disturbances have negatively affected woodland caribou populations (Rangifer tarandus caribou), which prefer to function in large undisturbed areas. We present a linear programming model that allocates a fixed-width corridor between isolated caribou ranges and estimates its impact

We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly \({\mathcal {N}}{\mathcal {P}}\)-hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use the Gaussian smoothing approach of Nesterov and Spokoiny(Found Comput Math 17(2): 527–566, 2015. https://doi.org/10.1007/s10208-015-9296-2) and extend their results, obtained for optimization methods for smooth zeroth-order non-convex problems

This paper is focused on solving an industrially-motivated, rich routing variant of the so-called full truckload pickup and delivery problem. It addresses a setting where the distributor has to transport full truckload shipments between distribution centers and customer locations, yet the distributor’s owned fleet is inadequate to perform the totality of the required deliveries and thus a subset of

The paper is mainly devoted to the theory of duality of boundary value problems (BVPs) for differential inclusions of higher orders. For this, on the basis of the apparatus of locally conjugate mappings in the form of Euler–Lagrange-type inclusions and transversality conditions, sufficient optimality conditions are obtained. Wherein remarkable is the fact that inclusions of Euler–Lagrange type for

In this paper, we propose a new modified subgradient extragradient method for solving equilibrium problems involving pseudomonotone and Lipchitz-type bifunctions in Hilbert spaces. We establish the strong convergence of the proposed method under several suitable conditions. In addition, the linear convergence is obained under strong pseudomonotonicity assumption. Our results generalize and extend some

This paper presents an approach to shortest path minimization for graphs with random weights of arcs. To deal with uncertainty we use the following risk measures: Probability of Exceedance (POE), Buffered Probability of Exceedance (bPOE), Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR). Minimization problems with POE and VaR objectives result in mixed integer linear problems (MILP) with two

Using a dual method for solving linear fractional programming problems, we propose an approach to find optimal solutions of linear countable semi-infinite fractional programming problems via optimizing sequences. Duality theorems are established. A dual scheme for solving linear countable semi-infinite fractional problems is proposed. Examples are provided.

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