The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in L1, L∞ and L2 norm. Extensive numerical experiments to ...

In this paper, we studies robust downlink beamforming for a multiuser multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system when only imperfect knowledge of the channel state information (CSI) is available at the transmitter. Specifically, we exploit two different models to describe CSI errors: a) deterministic bounded and b) stochastic random. ...

A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synt...

In this work, we consider the problem of learning a positive semidefinite matrix. The critical issue is how to preserve positive semidefiniteness during the course of learning. Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focusin...

This paper deals with several combinatorial optimization problems. The most challenging such problem is the quadratic assignment problem. It is considered in both two dimensions (QAP) and in three dimensions (Q3AP) and in the context of communication engineering. Semidefinite relaxations are used to derive lower bounds for the optimum while heuristics are applied to either find upper bounds or ...

We use the merit function technique to formulate a linearly constrained bilevel convex quadratic problem as a convex program with an additional convex-d.c. constraint. To solve the latter problem we approximate it by convex programs with an additional convex-concave constraint using an adaptive simplicial subdivision. This approximation leads to a branch-and-bound algorithm for finding a global...

We show that the problem of designing a quantum information processing error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to ...

We introduce a novel optimization method, semidefinite programming, to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hy...

The problem of determining whether quadratic programming models possess either unique or multiple optimal solutions is important for empirical analyses which use a mathematical programming framework. Policy recommendations which disregard multiple optimal solutions (when they exist) are potentially incorrect and less than efficient. This paper proposes a strategy and the associated algorithm fo...