In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

We study the problem of minimizing the sum of a smooth strongly convex function and a non-smooth convex function. We consider solving this problem using the proximal gradient (PG) method, which at each iteration uses the proximal operator with respect to the non-smooth convex function at the intermediate iterate obtained using the gradient with respect to the smooth strongly convex function. We...

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obt...

The range of a payoff function in an n-player finite strategic game is investigated using a novel approach, the notion of extreme points of a nonconvex set. A basic structural characteristic of a noncooperative payoff region is that any subregion must be non-strictly convex if it contains a relative neighborhood of a boundary point of the noncooperative payoff region. This can be proved efficie...

In this contribution we derive the cost function corresponding to the linear complexity Subtractive Interference Cancellation with tangent hyperbolic tentative decisions. We use the cost function to analyse the fix-points of solving the Subtractive Interference Cancellation equations. The analysis show that we can control the slope of the tangent hyperbolic functions so that the corresponding c...

in this paper particle swarm optimization with smart inertia factor (pso-sif) algorithm is proposed to solve combined heat and power economic dispatch (chped) problem. the chped problem is one of the most important problems in power systems and is a challenging non-convex and non-linear optimization problem. the aim of solving chped problem is to determine optimal heat and power of generating u...

The online optimization problem with non-convex loss functions over a closed convex set, coupled set of inequality (possibly non-convex) constraints is challenging learning problem. A proximal method multipliers quadratic approximations (named as OPMM) presented to solve this long term constraints. Regrets the violation Karush-Kuhn-Tucker conditions OPMM for solving problems are analyzed. Under...

A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the set enjoys uniform coverage over all non-decreasing regression functions. Furthermore, diameter automatically adapts to unknown number pieces true parameter, sense that bounded from above by minimax risk class $k$-piecewise constant The a increasing f...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.