The objective of the paper is to evaluate the impact of the infinity computing paradigm on practical solution of nonsmooth unconstrained optimization problems, where the objective function is assumed to be convex and not necessarily differentiable. For such family of problems, the occurrence of discontinuities in the derivatives may result in failures of the algorithms suited for smooth problem...

In this paper, we prove the complexity bounds for methods of Convex Optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most n times more iterations than the standard gradient methods, where n is the dimension of the space of variables. This conclusion is...

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

A semidefinite programming problem can be regarded as a convex nonsmooth optimization problem, so it can be represented as a semi-infinite linear programming problem. Thus, in principle, it can be solved using a cutting plane approach; we describe such a method. The cutting plane method uses an interior point algorithm to solve the linear programming relaxations approximately, because this resu...

Abstract Copositive optimization is a special case of convex conic programming, and it consists optimizing linear function over the cone all completely positive matrices under constraints. provides powerful relaxations NP-hard quadratic problems or combinatorial problems, but there are still many open regarding copositive matrices. In this paper, we focus on one such problem; finding (CP) facto...

The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, both assumptions. ALM may experience oscillations and divergence when underlying problem simultaneously nonconvex nonsmooth. In this paper, we consider linearly with a (in particular, weakly convex)...

In a Hilbert space setting, we consider new first order optimization algorithms which are obtained by temporal discretization of damped inertial autonomous dynamic involving dry friction. The function f to be minimized is assumed differentiable (not necessarily convex). friction potential $$ \varphi , has sharp minimum at the origin, enters algorithm via its proximal mapping, acts as soft thres...

In this paper we introduce a definition of approximate Pareto efficient solution as well necessary condition for such solutions in the multiobjective setting on Riemannian manifolds. We also propose an inexact proximal point method nonsmooth optimization context by using notion solution. The main convergence result ensures that each cluster (if any) any sequence generated is critical point. Fur...

A number of recent works have emphasized the prominent role played by the KurdykaLojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of a non necessarily convex differentiable function and a non necessaril...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...