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ProblemCourse & topicStatus
OPT:010117Mathematical problem title
Convex Optimization Hessian Quadratic FormConvex Optimization Amgm Unique Min
Convex sets, convex functions, and epigraph geometryConvex Optimization · Mixed review
—View access optionsConvex Optimization Lse Softmax GradientConvex Optimization Simplex Hessian Spectrum
Convex sets, convex functions, and epigraph geometryConvex Optimization · Mixed review
—View access optionsConvex Optimization Max Affine SubdifferentialConvex Optimization Support Membership
Separation, conjugates, and subgradientsConvex Optimization · Mixed review
—View access optionsConvex Optimization Box Euclidean ProjectionConvex Optimization Strict Separating Hyperplane
Separation, conjugates, and subgradientsConvex Optimization · Mixed review
—View access optionsConvex Optimization Log Barrier ProximalConvex Optimization Prox Derivative Bound
Optimality conditions, projections, and proximal operatorsConvex Optimization · Mixed review
—Optimality conditions, projections, and proximal operatorsConvex Optimization · Mixed review
—Lagrangian duality, constraint qualifications, and KKT theoryConvex Optimization · Mixed review
—Lagrangian duality, constraint qualifications, and KKT theoryConvex Optimization · Mixed review
—Lagrangian duality, constraint qualifications, and KKT theoryConvex Optimization · Mixed review
—First-order, Newton, and splitting methods with ratesConvex Optimization · Mixed review
—First-order, Newton, and splitting methods with ratesConvex Optimization · Mixed review
—First-order, Newton, and splitting methods with ratesConvex Optimization · Mixed review
—Conic, second-order cone, and semidefinite optimizationConvex Optimization · Mixed review
—Conic, second-order cone, and semidefinite optimizationConvex Optimization · Mixed review
—Conic, second-order cone, and semidefinite optimizationConvex Optimization · Mixed review
—Showing 15 of 15 matching problems.
The form e^x a^2+e^y b^2+e^{-x-y}(a+b)^2 is positive; AM-GM min 3 uniquely at 0; H(0) has eigs 1 and 3
LSE on R^3 has gradient p and Hessian diag(p)-pp^T; at 0 the eigs are 0,1/3,1/3 and the plane min is log 3 uniquely at 0
The subdifferential of max{x1,x2,0} at 0 is the triangle conv{e1,e2,0}; (0.4,0.3) is valid and (0.8,0.4) is not
The projection of (3,2) onto [-1,1]^2 is (1,1), distance sqrt(5); n=(2,1) supports at 3 and the midplane 11/2 is strict
The prox of -log is (v+sqrt(v^2+4 tau))/2; at v=1, tau=2 one obtains 2 with value -log 2+1/4, and the derivative stays in (0,1)
The unique minimizer of |x-1|+2|x+1|+(x-3)^2/2 is x=1 with value 6
The equality QP attains 2/5 at x*=(4/5,1/5) with multiplier nu*=-4/5 and zero gap
The LP and its dual both attain 10 uniquely at (2,2) and (2,1,0)
Three logs on x1+x2+x3=6 attain 3 log 2 uniquely at (2,2,2)
Gradient descent on (x1^2+9x2^2)/2 with step 1/5 first meets f<=0.01 at k=14
Newton on x-log x is x(2-x); the error obeys e+=-e^2 and the orbit from 1/2 is 3/4, 15/16, 255/256
Coordinate descent on (1/2)(x^2+xy+y^2) from (0,1) has yk=4^{-k} and fk=(3/2)16^{-k}
The SOC projection of (1,3,4) is (3,9/5,12/5); the residual in -K is orthogonal of norm 2sqrt2
The robust value aTx+||PTx|| at (1,2) is 1+2sqrt2; robust<=4 is an SOC with slack 3-2sqrt2
The min enclosing circle of (-1,0),(1,0),(0,2) has center (0,3/4), radius 5/4, and KKT weights 5/16,5/16,3/8