Complexity of Convex Optimization Using Geometry Based Measures And a Reference
Complexity of Convex Optimization Using Geometry Based Measures And a Reference
Robert Michael Freund
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1 of [5]), and together with (12) this then implies that sym(u', r) > 3-5^5^:1-25 ■ GEOMETRY-BASED COMPLEXITY 9 Remark 2. 1 Note tliat (11) implies that for any objective function vector seX': maxs^w - s^w I ) ( s^w — mills'^ u; ) . (14) w€T ~ Vs. 5(9 + 1. 25/ V weT J 3 Complexity of Computing a Feasible Solu- tion of Gp In this section we present and analyze algorithm FEAS for computing a feasible solution of Gp using the barrier method in equation-solving mode. The output of algorithm FEAS w...ill be a point x that will satisfy . 4x = 6, x G P, as well as several other important properties that will be described in this section. The computed point x will also be used to initiate algorithm OPT, to be presented in Section 4, that will start from x and will then compute an e-optimal solution of Gp. Algorithm FEAS will employ the barrier method in equation-solving mode to solve the following optimization problem denoted by Pi: Pi : t' := maximum^ ( t [lb) s.
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