We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Neverthele...

Roos proved that the devised full-step infeasible algorithm has O(n) worst-case iteration complexity. This complexity bound depends linearly on a parameter ¯ κ(ζ), which is proved to be less than √ 2n. Based on extensive computational evidence (hundreds of thousands of randomly generated problems), Roos conjectured that ¯ κ(ζ) = 1 (Conjecture 5.1 in the above-mentioned paper), which would yield...

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

It is well known that it very difficult to solve constrained multiobjective optimization problems. Such problems not only need optimize the objective function but also consider constraints. The epsilon constraint handling method commonly used, which releases degree of violations by defining a gradually decayed epsilon. However, for solutions whose overall greater than epsilon, original cannot g...

In this paper, a new predictor-corrector method is proposed for solving sufficient linear complementarity problems (LCP) with an infeasible starting point. The method generates a sequence of iterates in a wide and symmetric neighborhood of the infeasible central path of the LCP. If the starting point is feasible or close to being feasible, then an ε-approximate solution is obtained in at most O...

We combine interior-point methods and results from matrix completion theory in an approximate method for the large dense quadratic programming problems that arise in support vector machine training. The basic idea is to replace the dense kernel matrix with the maximum determinant positive definite completion of a subset of the entries of the kernel matrix. The resulting approximate kernel matri...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

in this paper, a combinational optimization algorithm is introduced to obtain the best size and location of static compensator (statcom) in power systems. its main contribution is considering contingency analysis where lines outages may lead to infeasible solutions especially at peak loads and it commonly can be vanished by load-shedding. the objective of the proposed algorithm is firstly to pr...

Abstract In this paper, we suggest a new infeasible interior-point method (IIPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -linear complementarity problem ( -LCP) based on class of kernel func...