The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems

From MaRDI portal
Publication:1772961

DOI10.1007/s10479-004-5022-1zbMath1116.90122OpenAlexW1990494141MaRDI QIDQ1772961

Hoai An Le Thi, Tao Pham Dinh

Publication date: 22 April 2005

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10479-004-5022-1




Related Items

Robust spherical separationA DC approach for minimax fractional optimization programs with ratios of convex functionsRobust piecewise linear L1-regression via nonsmooth DC optimizationComposite Difference-Max Programs for Modern Statistical Estimation ProblemsImage Segmentation via Fischer-Burmeister Total Variation and ThresholdingConvexification with Bounded Gap for Randomly Projected Quadratic OptimizationSimultaneous Grouping Pursuit and Feature Selection Over an Undirected GraphDifference-of-Convex Learning: Directional Stationarity, Optimality, and SparsitySparse optimization via vector \(k\)-norm and DC programming with an application to feature selection for support vector machinesA random covariance model for bi‐level graphical modeling with application to resting‐state fMRI dataCenter-Augmented ℓ2-Type Regularization for Subgroup LearningA mesh‐based partitioning algorithm for decreasing conservatism in solving bilinear matrix inequality problemsBilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systemsAdaptively weighted difference model of anisotropic and isotropic total variation for image denoisingFinding robust minimizer for non-convex phase retrievalLearning Markov Models Via Low-Rank OptimizationThe descent algorithm for solving the symmetric eigenvalue complementarity problemAccelerated sparse recovery via gradient descent with nonlinear conjugate gradient momentumSteering exact penalty DCA for nonsmooth DC optimisation problems with equality and inequality constraintsSorted \(L_1/L_2\) minimization for sparse signal recoveryStrong substitutes: structural properties, and a new algorithm for competitive equilibrium pricesA wonderful triangle in compressed sensingA Based-DC Programming Approach for Planning a Multisensor Multizone Search for a Moving TargetA DC Algorithm for Solving Quadratic-linear Bilevel Optimization ProblemsA DC Programming Approach for Sparse Estimation of a Covariance MatrixA New Approach for Optimizing Traffic Signals in Networks Considering ReroutingSolving the Quadratic Eigenvalue Complementarity Problem by DC ProgrammingThe Maximum Ratio Clique Problem: A Continuous Optimization Approach and Some New ResultsImplicit regularization effects of the Sobolev norms in image processingSemi-supervised \(k\)-means clustering via DC programming approachConvergence rate analysis of an extrapolated proximal difference-of-convex algorithmStructured model selection via ℓ1−ℓ2 optimizationFirst order inertial optimization algorithms with threshold effects associated with dry frictionDCA approaches for simultaneous wireless information power transfer in MISO secrecy channelA refined inertial DC algorithm for DC programmingLARGE SYSTEM OF SEEMINGLY UNRELATED REGRESSIONS: A PENALIZED QUASI-MAXIMUM LIKELIHOOD ESTIMATION PERSPECTIVEOn solving difference of convex functions programs with linear complementarity constraintsA Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image LabelingA proximal bundle method for a class of nonconvex nonsmooth composite optimization problemsA variable metric and Nesterov extrapolated proximal DCA with backtracking for a composite DC programSolving nonmonotone affine variational inequalities problem by DC programming and DCAOn a solution method in indefinite quadratic programming under linear constraintsOpen issues and recent advances in DC programming and DCALikelihood Ratio Tests for a Large Directed Acyclic GraphOne-dimensional phase retrieval: regularization, box relaxation and uniquenessBlock Clustering Based on Difference of Convex Functions (DC) Programming and DC AlgorithmsSpontaneous Clustering via Minimum Gamma-DivergenceOnline Learning Based on Online DCA and Application to Online ClassificationEfficient Nonnegative Matrix Factorization by DC Programming and DCADC Algorithm for Extended Robust Support Vector MachineSparse Covariance Matrix Estimation by DCA-Based AlgorithmsA DC Programming Approach for Finding Communities in NetworksOn Recent Progress in Shakedown Analysis and Applications to Large-Scale ProblemsNonsmooth DC programming approach to clusterwise linear regression: optimality conditions and algorithmsDecomposition Methods for Computing Directional Stationary Solutions of a Class of Nonsmooth Nonconvex Optimization ProblemsExtension of primal-dual interior point methods to diff-convex problems on symmetric conesQuantile Regression for Analyzing Heterogeneity in Ultra-High DimensionCalibrating low-rank correlation matrix problem: an SCA-based approachOptimization-based stability analysis of structures under unilateral constraintsSequential Convex Programming for Computing Information-Theoretic Minimal Partitions: Nonconvex Nonsmooth OptimizationDouble Bundle Method for finding Clarke Stationary Points in Nonsmooth DC ProgrammingDC programming approaches for discrete portfolio optimization under concave transaction costsOptimizing sensor cover energy via DC programmingOn the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions MethodsForewordEssentials of numerical nonsmooth optimizationDC programming approach for portfolio optimization under step increasing transaction costsStochastic DCA for Sparse Multiclass Logistic RegressionDC Programming and DCA for Enhancing Physical Layer Security in Amplify-and-Forward Relay Beamforming Networks Based on the SNR ApproachSingle Straddle Carrier Routing Problem in Port Container Terminals: Mathematical Model and Solving ApproachesA DC Programming Approach for Mixed-Integer Linear ProgramsDesign of Highly Nonlinear Balanced Boolean Functions Using an Hybridation of DCA and Simulated Annealing AlgorithmTwo-Stage Stochastic Programming with Linearly Bi-parameterized Quadratic RecourseOn Algorithms for Difference of Monotone OperatorsOn Algorithms for Difference of Monotone OperatorsThe Boosted Difference of Convex Functions Algorithm for Nonsmooth FunctionsAn interior proximal linearized method for DC programming based on Bregman distance or second-order homogeneous kernelsDC Programming and DCA for Challenging Problems in Bioinformatics and Computational BiologyNew regularity conditions and Fenchel dualities for DC optimization problems involving composite functionsThe Primal-Dual Hybrid Gradient Method for Semiconvex SplittingsAlgorithmic versatility of SPF-regularization methodsLearnable Descent Algorithm for Nonsmooth Nonconvex Image ReconstructionUnnamed ItemEssentials of numerical nonsmooth optimizationEfficient Boosted DC Algorithm for Nonconvex Image Restoration with Rician NoiseNew Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol ModelAsymptotic Properties of Stationary Solutions of Coupled Nonconvex Nonsmooth Empirical Risk MinimizationStochastic Difference-of-Convex-Functions Algorithms for Nonconvex ProgrammingA subgradient-based convex approximations method for DC programming and its applicationsSolving partitioning-hub location-routing problem using DCAAlternating DC algorithm for partial DC programming problemsSolving continuous min max problem for single period portfolio selection with discrete constraints by DCAA new semi-supervised classifier based on maximum vector-angular marginTraining robust support vector regression with smooth non-convex loss functionA unified DC programming framework and efficient DCA based approaches for large scale batch reinforcement learningThe DTC (difference of tangentially convex functions) programming: optimality conditionsA polynomial local optimality condition for the concave piecewise linear network flow problemAn inexact proximal DC algorithm with sieving strategy for rank constrained least squares semidefinite programmingDC semidefinite programming and cone constrained DC optimization. I: TheoryA new efficient algorithm based on DC programming and DCA for clusteringApplication of lower bound direct method to engineering structuresClassification in the multiple instance learning framework via spherical separationSparse signal recovery via generalized Gaussian functionA continuous DC programming approach to the strategic supply chain design problem from qualified partner setOptimization based DC programming and DCA for hierarchical clusteringA generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problemLarge-scale standard pooling problems with constrained pools and fixed demandsNonconvex and nonsmooth approaches for affine chance-constrained stochastic programsDC Programming and DCA for General DC ProgramsDC Programming Approaches for BMI and QMI Feasibility ProblemsA DC Programming Approach for Sparse Linear Discriminant AnalysisThe Confrontation of Two Clustering Methods in Portfolio Management: Ward’s Method Versus DCA MethodBinary classification via spherical separator by DC programming and DCAA unifying framework of high-dimensional sparse estimation with difference-of-convex (DC) regularizationsAlternating DCA for reduced-rank multitask linear regression with covariance matrix estimationA proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planesGeneral variational inclusions involving difference of operatorsSolving the index tracking problem: a continuous optimization approachGroup variable selection via \(\ell_{p,0}\) regularization and application to optimal scoringA selective strategy for shakedown analysis of engineering structuresA sub-additive DC approach to the complementarity problemThe boosted DC algorithm for linearly constrained DC programmingOn subdifferentials via a generalized conjugation scheme: an application to DC problems and optimality conditionsUsing positive spanning sets to achieve d-stationarity with the boosted DC algorithmRegularized quantile regression for ultrahigh-dimensional data with nonignorable missing responsesSolution methodologies for minimizing a sum of pointwise minima of two functionsClusterwise support vector linear regressionA DC Programming Approach to the Continuous Equilibrium Network Design ProblemDC Programming and DCA for Transmit Beamforming and Power Allocation in Multicasting Relay NetworkSolving an Infinite-Horizon Discounted Markov Decision Process by DC Programming and DCAAn efficient DCA based algorithm for power control in large scale wireless networksOn solving the sum-of-ratios problemSequential difference-of-convex programmingRobust regularized extreme learning machine for regression with non-convex loss function via DC programAn incremental bundle method for portfolio selection problem under second-order stochastic dominanceA new nonconvex approach for image restoration with Gamma noiseError bound and isocost imply linear convergence of DCA-based algorithms to D-stationarityDeep CNN denoiser prior for blurred images restoration with multiplicative noiseThe Toland-Fenchel-Lagrange duality of DC programs for composite convex functionsA DC programming approach for sensor network localization with uncertainties in anchor positionsNotes on the difference of two monotone operatorsComputing B-Stationary Points of Nonsmooth DC ProgramsConvergence analysis of a proximal point algorithm for minimizing differences of functionsA DC programming approach for feature selection in support vector machines learningPortfolio optimization model with and without options under additional constraintsIncremental DC optimization algorithm for large-scale clusterwise linear regressionDCA-based algorithms for DC fittingNew quadratic lower bound for multivariate functions in global optimizationOptimality conditions and DC-Dinkelbach-type algorithm for generalized fractional programs with ratios of difference of convex functionsDC programming and DCA for enhancing physical layer security via relay beamforming strategiesA difference-of-convex programming approach with parallel branch-and-bound for sentence compression via a hybrid extractive modelAn augmented subgradient method for minimizing nonsmooth DC functionsRobust investment strategies with discrete asset choice constraints using DC programmingOne step from DC optimization to DC mixed variational inequalitiesInformation projection on Banach spaces with applications to state independent KL-weighted optimal controlNovel DCA based algorithms for a special class of nonconvex problems with application in machine learningA new concave reformulation and its application in solving DC programming globally under uncertain environmentA continuous approach for the concave cost supply problem via DC programming and DCALong-short portfolio optimization under cardinality constraints by difference of convex functions algorithmGlobally convergent DC trust-region methodsA difference of convex formulation of value-at-risk constrained optimizationA closedness condition and its applications to DC programs with convex constraintsA class of semi-supervised support vector machines by DC programmingOptical FlowAn inertial algorithm for DC programmingSemisupervised spherical separationOn critical points of the difference of two maximal monotone operatorsRobustness of learning algorithms using hinge loss with outlier indicatorsDC Approximation Approach for ℓ0-minimization in Compressed SensingDC Programming and DCA Approach for Resource Allocation Optimization in OFDMA/TDD Wireless NetworksDC Programming and DCA for a Novel Resource Allocation Problem in Emerging Area of Cooperative Physical Layer SecurityOn DC based methods for phase retrievalFeature selection in SVM via polyhedral \(k\)-normSolving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximationsOn functions determined by dense setsStochastic DCA for minimizing a large sum of DC functions with application to multi-class logistic regressionSequential parametric convex approximation algorithm for bilinear matrix inequality problemA difference of convex optimization algorithm for piecewise linear regressionSplit proximal linearized algorithm and convergence theorems for the split DC programAnalysis of generalized Bregman surrogate algorithms for nonsmooth nonconvex statistical learningA DC programming approach for solving a centralized group key management problemRegularity conditions characterizing Fenchel-Lagrange duality and Farkas-type results in DC infinite programmingA non-convex algorithm framework based on DC programming and DCA for matrix completionOptimal replenishment order placement in a finite time horizonPolyhedral separation via difference of convex (DC) programmingEfficient DC programming approaches for the asymmetric eigenvalue complementarity problemLearning sparse classifiers with difference of convex functions algorithmsK-means clustering via a nonconvex optimization approachOn the problem polyhedral separability: a numerical solutionInertial proximal algorithm for difference of two maximal monotone operatorsRobust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approachHybrid proximal linearized algorithm for the split DC program in infinite-dimensional real Hilbert spacesGeneralized Farkas' lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimizationMM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selectionCommunity detection via an efficient nonconvex optimization approach based on modularityOptimality conditions and a method of centers for minimax fractional programs with difference of convex functionsBundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraintsOn local search in d.c. optimization problemsDC programming techniques for solving a class of nonlinear bilevel programsDCA based algorithms for multiple sequence alignment (MSA)On difference of two monotone operatorsDC approximation approaches for sparse optimizationDifference of convex functions algorithms (DCA) for image restoration via a Markov random field modelOn numerical solving the spherical separability problemGlobal convergence of a proximal linearized algorithm for difference of convex functionsPoint source super-resolution via non-convex \(L_1\) based methodsVariational multiplicative noise removal by DC programmingA DC programming approach for planning a multisensor multizone search for a targetA continuous DC programming approach for resource allocation in OFDMA/TDD wireless networksDC programming and DCA for solving Brugnano-Casulli piecewise linear systemsDC programming and DCA for enhancing physical layer security via cooperative jammingSupervised classification and mathematical optimizationHomogeneity detection for the high-dimensional generalized linear modelOptimization with a class of multivariate integral stochastic order constraintsDCA for solving the scheduling of lifting vehicle in an automated port container terminalAn efficient combined DCA and B\&B using DC/SDP relaxation for globally solving binary quadratic programsDC models for spherical separationA difference of convex functions algorithm for optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processorsSolving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCAMargin maximization in spherical separationValue-at-risk optimization using the difference of convex algorithmGlobal optimization for optimal power flow over transmission networksA framework for optimization under ambiguityFeature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithmsOn some geometric conditions for minimality of DCH-functions via DC-duality approachFeature selection in machine learning: an exact penalty approach using a difference of convex function algorithmTotal Lagrange duality for DC infinite optimization problemsAlgorithms for linear programming with linear complementarity constraintsOptimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimizationAn efficient DC programming approach for portfolio decision with higher momentsOn solving linear complementarity problems by DC programming and DCAAsymptotic closure condition and Fenchel duality for DC optimization problems in locally convex spacesNew and efficient DCA based algorithms for minimum sum-of-squares clusteringEfficient estimation of approximate factor models via penalized maximum likelihoodNew formulations of the multiple sequence alignment problemProperties of two DC algorithms in quadratic programmingThe directional subdifferential of the difference of two convex functionsShakedown analysis with multidimensional loading spacesExact penalty and error bounds in DC programmingA DC programming approach for solving the symmetric eigenvalue complementarity problemDC programming algorithm for clusterwise linear \(L_1\) regressionOn global optimization with indefinite quadraticsStable zero Lagrange duality for DC conic programmingA branch-and-bound algorithm embedded with DCA for DC programmingA combined DCA: GA for constructing highly nonlinear balanced Boolean functions in cryptographyThe space decomposition theory for a class of eigenvalue optimizationsD.C. programming approach for solving an applied ore-processing problemFarkas' lemma: three decades of generalizations for mathematical optimizationOptimizing a multi-stage production/inventory system by DC programming based approachesAnalysis sparse representation for nonnegative signals based on determinant measure by DC programmingFuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithmsConvergence analysis of difference-of-convex algorithm with subanalytic dataSolving DC programs using the cutting angle methodOn the pervasiveness of difference-convexity in optimization and statisticsOn the difference of two maximal monotone operators: Regularization and algorithmic approachesA redistributed bundle algorithm based on local convexification models for nonlinear nonsmooth DC programmingSignal and image approximation with level-set constraintsA proximal difference-of-convex algorithm with extrapolationDCA based algorithms for feature selection in multi-class support vector machineDC programming and DCA: thirty years of developmentsAccelerating the DC algorithm for smooth functionsVisualizing data as objects by DC (difference of convex) optimizationDC formulations and algorithms for sparse optimization problemsOn minimizing difference of a SOS-convex polynomial and a support function over a SOS-concave matrix polynomial constraintA study of the difference-of-convex approach for solving linear programs with complementarity constraintsSolving the degree-concentrated fault-tolerant spanning subgraph problem by DC programmingRobust multicategory support vector machines using difference convex algorithmA biobjective approach to recoverable robustness based on location planningMinimizing nonsmooth DC functions via successive DC piecewise-affine approximationsAggregate subgradient method for nonsmooth DC optimizationGlobally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approachesThe hill detouring method for minimizing hinging hyperplanes functionsNoisy Euclidean distance matrix completion with a single missing nodeImproved dc programming approaches for solving the quadratic eigenvalue complementarity problemThe DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problemsConsistency bounds and support recovery of d-stationary solutions of sparse sample average approximationsA sequential partial linearization algorithm for the symmetric eigenvalue complementarity problemExtensions on ellipsoid bounds for quadratic integer programmingSelf-organizing maps by difference of convex functions optimizationDictionary learning for fast classification based on soft-thresholdingOn the subdifferentiability of the difference of two functions and local minimizationNew and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chainsError bounds for the difference of two convex multifunctionsFunctional inequalities and theorems of the alternative involving composite functionsPortfolio selection under downside risk measures and cardinality constraints based on DC programming and DCADC programming and DCA for globally solving the value-at-riskOptimality conditions and duality for DC programming in locally convex spacesDouble regularization methods for robust feature selection and SVM classification via DC programming



Cites Work


This page was built for publication: The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems