Globally convergent evolution strategies for constrained optimization

International audienceIn this paper we propose, analyze, and test algorithms for constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function.The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints.The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses the particular cases of bounds on the variables and linear constraints. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness

Point Spread Function Estimation for a Terahertz Imaging System

We present a method for estimating the point spread function of a terahertz imaging system designed to operate in reflection mode. The method is based on imaging phantoms with known geometry, which have patterns with sharp edges at all orientations. The point spread functions are obtained by a deconvolution technique in the Fourier domain. We validate our results by using the estimated point spread functions to deblur several images of natural scenes and by direct comparison with a point source response. The estimations turn out to be robust and produce consistent deblurring quality over the entire depth of the focal region of the imaging system.</p

Feasible Sequential Quadratic Programming For Finely Discretized Problems From Sip

A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized Semi-Infinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP sub-problems at each iteration, and (ii) that every iterate satisfies all constraints. 1 INTRODUCTION Consider the Semi-Infinite Programming (SIP) problem minimize f(x) subject to \Phi(x) 0; (SI) where f : IR n ! IR is continuously differentiable, and \Phi : IR n ! IR is defined by \Phi(x) \Delta = sup ¸2[0;1] OE(x; ¸); with OE : IR n \Theta [0; 1] ! IR continuously differentiable in the first argument. For an excellent survey of the theory behind the problem (SI), in addition to some algorithms and applications, see [9] as well as the other papers in the present volume. Many globally convergent algorithms designed to solve (SI) 2 Chapter 1..