Mixed quasi invex equilibrium problems.
Modified T-F function method for finding global minimizer on unconstrained optimization.
Nature–inspired metaheuristic algorithms to find near–OGR sequences for WDM channel allocation and their performance comparison
Nowadays, nature–inspired metaheuristic algorithms are most powerful optimizing algorithms for solving the NP–complete problems. This paper proposes three approaches to find near–optimal Golomb ruler sequences based on nature–inspired algorithms in a reasonable time. The optimal Golomb ruler (OGR) sequences found their application in channel–allocation method that allows suppression of the crosstalk due to four–wave mixing in optical wavelength division multiplexing systems. The simulation results...
New technique for solving univariate global optimization
In this paper, a new global optimization method is proposed for an optimization problem with twice differentiable objective function a single variable with box constraint. The method employs a difference of linear interpolant of the objective and a concave function, where the former is a continuous piecewise convex quadratic function underestimator. The main objectives of this research are to determine the value of the lower bound that does not need an iterative local optimizer. The proposed method...
Nonlinear nonconvex optimization by evolutionary algorithms applied to robust control.
On a Class of Nonconvex Problems Where all Local Minima are Global
On convergence of a global search strategy for reverse convex problems.
On generalized monotone multifunctions with applications to optimality conditions in generalized convex programming.
On maximizing a concave function subject to linear constraints by Newton's method
On semidefinite bounds for maximization of a non-convex quadratic objective over the l1 unit ball
We consider the non-convex quadratic maximization problem subject to the l1 unit ball constraint. The nature of the l1 norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.
On the connectivity of efficient point sets
The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.
On the quadratic fractional optimization with a strictly convex quadratic constraint
In this paper, we have studied the problem of minimizing the ratio of two indefinite quadratic functions subject to a strictly convex quadratic constraint. First utilizing the relationship between fractional and parametric programming problems due to Dinkelbach, we reformulate the fractional problem as a univariate equation. To find the root of the univariate equation, the generalized Newton method is utilized that requires solving a nonconvex quadratic optimization problem at each iteration. A...
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter...
Optimization problem under two-sided (max, +)/(min, +) inequality constraints
-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form , where , , are real numbers. Similarly -linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have -linear functions of variables on one side and -linear functions of variables on the other side. Such systems can be applied...
Outcome space range reduction method for global optimization of sum of affine ratios problem
Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large...
Parallelization of artificial immune systems using a massive parallel approach via modern GPUs
Parallelization is one of possible approaches for obtaining better results in terms of algorithm performance and overcome the limits of the sequential computation. In this paper, we present a study of parallelization of the opt-aiNet algorithm which comes from Artificial Immune Systems, one part of large family of population based algorithms inspired by nature. The opt-aiNet algorithm is based on an immune network theory which incorporates knowledge about mammalian immune systems in order to create...
Perturbation theory of duality in vector nonconvex optimization via the abstract duality scheme
Production games, core deficit, duality and shadow prices
Considered here are production (or market) games with transferable utility. Prime objects are explicitly computable core solutions, or somewhat "deficit" versions of such, fully defined by shadow prices. Main arguments revolve around standard Lagrangian duality. A chief concern is to relax, or avoid, the commonplace assumption that all preferences and production possibilities be convex. Doing so, novel results are obtained about non-emptiness of the core, and about specific imputations therein.
Proximal smoothness and the lower- property.