Enhancing Lagrangian Dual Optimization for Linear Programs by Obviating Nondifferentiability
Published Online:1 Feb 2007https://doi.org/10.1287/ijoc.1050.0158
References
- Mixed-integer bilinear-programming problems. Math. Programming (1993) 59:279–305Crossref, Google Scholar
- The volume algorithm: Producing primal solutions with a subgradient method. Math. Programming (2000) 87:385–399Crossref, Google Scholar
- Linear Programming and Network Flows (2005) 3rd ed.(Wiley, New York) Google Scholar
- Nonlinear Programming: Theory and Algorithms (2006) 3rd ed.(Wiley, New York) Crossref, Google Scholar
- On improving relaxation methods by modified gradient techniques. Math. Programming Stud. (1975) 3:26–34Crossref, Google Scholar
- The Lagrangian relaxation method for solving integer programming problems. Management Sci. (1981) 27:1–18Link, Google Scholar
- Function minimization by conjugate gradients. Comput. J. (1964) 7:149–154Crossref, Google Scholar
- Validation of subgradient optimization. Math. Programming (1974) 6:62–88Crossref, Google Scholar
- Methods of conjugate gradients for solving linear systems. J. Res. National Bureau Standards, Section B (1952) 48:409–436Crossref, Google Scholar
- Ergodic, primal convergence in dual subgradient schemes for convex programming. Math. Programming (1999) 86:283–312Crossref, Google Scholar
- , Lemarechal C., Mifflin R. Bundle methods in nonsmooth optimization. Proc. IIASA Workshop, Laxenburg, Austria (1977) 3:79–109Google Scholar
- Nondifferentiable optimization of Lagrangian dual formulations for linear programs with recovery of primal solutions. (2004) . Ph.D. dissertation, Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VAGoogle Scholar
- Convergence and computational analyses for some variable target value and subgradient deflection methods. Comput. Optim. Appl. (2006) 34:409–428Crossref, Google Scholar
- Survey of bundle methods for nonsmooth optimization. Optim. Methods Software (2002) 17:1–29Crossref, Google Scholar
- An algorithm for constrained optimization with semismooth functions. Math. Oper. Res. (1977) 2:191–207Link, Google Scholar
- Smooth minimization of non-smooth functions. Math. Programming (2005) 103:127–152Crossref, Google Scholar
- Note on the convergence of methods of conjugate directions. Rev. Française d’Informatique Recherche Operationelle (1969) 3:35–43Google Scholar
- A general method of solving extremum problems. Soviet Math. (1967) 8:593–597Google Scholar
- Minimization of unsmooth functionals. USSR Comput. Math. Math. Phys. (1969) 9:14–29Crossref, Google Scholar
- Restart procedures for the conjugate gradient method. Math. Programming (1977) 12:241–254Crossref, Google Scholar
- Conjugate gradient methods with inexact searches. Math. Oper. Res. (1978) 3:244–256Link, Google Scholar
- Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs. Oper. Res. Lett. (1996) 19:105–113Crossref, Google Scholar
- Dual formulations and subgradient optimization strategies for linear programming relaxations of mixed-integer programs. Discrete Appl. Math. (1988) 20:51–68Crossref, Google Scholar
- New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems. Oper. Res. Lett. (1997) 21:1–9Crossref, Google Scholar
- A primal-dual conjugate subgradient algorithm for specially structured linear and convex programming problems. Appl. Math. Optim. (1989) 20:193–221Crossref, Google Scholar
- Conjugate gradient methods using quasi-Newton updates with inexact line searches. J. Math. Anal. Appl. (1990) 150:359–377Crossref, Google Scholar
- Limited memory space dilation and reduction algorithms. Comput. Optim. Appl. (2001) 19:55–77Crossref, Google Scholar
- A variable target value method for nondifferentiable optimization. Oper. Res. Lett. (2000) 26:1–8Crossref, Google Scholar
- Utilization of the operation of space dilatation in the minimization of convex functions. Kibernetika (1970a) 6:6–12Google Scholar
- Convergence rate of the gradient descent method with dilatation of the space. Kibernetika (1970b) 6:80–85Google Scholar
- Minimization Methods for Non-Differentiable Functions (1985) (Springer-Verlag, New York) Crossref, Google Scholar

