A note on an algorithm for generalized fractional programs
Journal of Optimization Theory and Applications
Convergence of some algorithms for convex minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Prox-regularization methods for generalized fractional programming
Journal of Optimization Theory and Applications
Proximal Point Methods and Nonconvex Optimization
Journal of Global Optimization
Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control
SIAM Journal on Optimization
A Bundle Method for Solving Variational Inequalities
SIAM Journal on Optimization
A bundle method for solving equilibrium problems
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Computing proximal points of nonconvex functions
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
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In this paper, we present several new implementable methods for solving a generalized fractional program with convex data. They are Dinkelbach-type methods where a prox-regularization term is added to avoid the numerical difficulties arising when the solution of the problem is not unique. In these methods, at each iteration a regularized parametric problem is solved inexactly to obtain an approximation of the optimal value of the problem. Since the parametric problem is nonsmooth and convex, we propose to solve it by using a classical bundle method where the parameter is updated after each `serious step'. We mainly study two kinds of such steps, and we prove the convergence and the rate of convergence of each of the corresponding methods. Finally, we present some numerical experience to illustrate the behavior of the proposed algorithms, and we discuss the practical efficiency of each one.