Solve c part optimization problem (c) Consider the following conic problem in variables (x1,x2) with the Lorentz cone L3:X1min { x1 +2x2 |X2(P1)X1+x2(i) Decide whether the problem is strictly feasible and bounded below. Draw the feasibleregion and, if available, find an optimal solution. Find the optimal objective value.(ii) Formulate the dual problem to (P1).(iii) Find at least one point in the dual feasible region that is(1) strictly feasible;(2) feasible but not strictly feasible. 1.(a) Let K CR" be a proper cone. Prove that the relation a - bEK is reflexive, antisymmetricand transitive on R".(b) Consider the following two sets of symmetric matrices:C = {A € S" | x"Ax > 0 Vx €R", x> 0}%3DandkP = {A € S" | A = £ ®(z®)", z® eR", ¿0 > 0, i = 1,..,k} .%3Di=1Prove:(i) C and P are cones.(ii) Show that C C P*, where P* is the dual cone to P.(c) Consider the following conic problem in variables (x1,x2) with the Lorentz cone L3:X1min { x1 +2x2 |X2(P1)x1+x2(i) Decide whether the problem is strictly feasible and bounded below. Draw the feasibleregion and, if available, find an optimal solution. Find the optimal objective value.(ii) Formulate the dual problem to (P1).(iii) Find at least one point in the dual feasible region that is(1) strictly feasible;(2) feasible but not strictly feasible.LM Advanced Management MathematicsTurn over

(c) Consider the following conic problem in variables (x1,x2) with the Lorentz cone L³: min { x1 +2x2 | X2 (P1) X1 +x2 (i) Decide whether the problem is strictly feasible and bounded below. Draw the feasible region and, if available, find an optimal solution. Find the optimal objective value. (ii) Formulate the dual problem to (P1). (iii) Find at least one point in the dual feasible region that is (1) strictly feasible; (2) feasible but not strictly feasible.

(c) Consider the following conic problem in variables (x1,x2) with the Lorentz cone L³: min { x1 +2x2 | X2 (P1) X1 +x2 (i) Decide whether the problem is strictly feasible and bounded below. Draw the feasible region and, if available, find an optimal solution. Find the optimal objective value. (ii) Formulate the dual problem to (P1). (iii) Find at least one point in the dual feasible region that is (1) strictly feasible; (2) feasible but not strictly feasible.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.

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