In this paper we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints, a major improvement over existing approaches, which either solve the problem in only a local neighborhood of the user initial guess through nonline...

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior know...

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimizatio...

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...

Based on credibilistic value-at-risk (CVaR) of regularfuzzy variable, we introduce a new CVaR reduction method fortype-2 fuzzy variables. The reduced fuzzy variables arecharacterized by parametric possibility distributions. We establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. The convex properties of second order moments with ...

During the last years, kernel based methods proved to be very successful for many real-world learning problems. One of the main reasons for this success is the efficiency on large data sets which is a result of the fact that kernel methods like Support Vector Machines (SVM) are based on a convex optimization problem. Solving a new learning problem can now often be reduced to the choice of an ap...

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods....

Let D be a DAG and let X be any non-empty subset of D’s vertices. X is a convex set of D if D contains no path that originates in X , then visits one or more vertices not in X , and then re-enters X . This work presents basic convexity algorithms for creating, growing, and shrinking convex sets using two different approaches: predecessor and successor sets, and topological sorts. It shows that ...

In this paper, we present a study on the sensitivity of aggregation methods with respect to the weights associated with objective functions of a multiobjective optimization problem. To do this study, we have developped some measurements such as the speed metric or the distribution metric. We have performed this study on a set of biobjective optimization test problems: a convex, a non-convex, a ...

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semiinfinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG in...