In this paper we consider the Convex Quadratic Optimization problem with simultaneous perturbation in the right-hand-side of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions are investigated as well as the behavior of the optimal value function on the regions. We show that identifying these regions can be done...

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of ...

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the cartesian product of several standard simplices (of possibly different dimensions). Two converging monotone interior point methods are established. Further, we prove...

Ill posed quadratic optimization frequently occurs in control and inverse problems and are not covered by the Lax-Milgram-Riesz theory. Typically small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the ‘hidden connection’ between the optimization problem and t...

Suitable solutions for multi-objective optimization problems are investigated as a set of solutions in the literature, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. The proposed algorithm in this paper is a hybrid of the particle swarm optimization algorithm [1] and a random search technique with quadratic approximation formula[2] n...

We derive computationally tractable formulations of the robust counterparts convex quadratic and conic constraints that are concave in matrix-valued uncertain parameters. do this for a broad range uncertainty sets. Our results provide extensions to known from literature. also consider hard constraints: those For counterpart such constraints, we inner outer approximations. As an application, sho...